{"id":1866,"date":"2018-12-11T13:35:13","date_gmt":"2018-12-11T18:35:13","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/find-the-equation-of-a-line\/"},"modified":"2018-12-11T13:35:13","modified_gmt":"2018-12-11T18:35:13","slug":"find-the-equation-of-a-line","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/find-the-equation-of-a-line\/","title":{"raw":"Find the Equation of a Line","rendered":"Find the Equation of a Line"},"content":{"raw":"\n[latexpage]<div class=\"textbox textbox--learning-objectives\"><h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>By the end of this section, you will be able to: <ul><li>Find an equation of the line given the slope and \\(y\\text{-intercept}\\)<\/li><li>Find an equation of the line given the slope and a point<\/li><li>Find an equation of the line given two points<\/li><li>Find an equation of a line parallel to a given line<\/li><li>Find an equation of a line perpendicular to a given line<\/li><\/ul><\/div><div data-type=\"note\" id=\"fs-id1167836287977\" class=\"be-prepared\"><p id=\"fs-id1167836532223\">Before you get started, take this readiness quiz.<\/p><ol id=\"fs-id1167836546304\" type=\"1\"><li>Solve: \\(\\frac{2}{5}\\left(x+15\\right).\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/987da0d0-2366-47d6-aa25-904e24991866#fs-id1167829789060\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Simplify: \\(-3\\left(x-\\left(-2\\right)\\right).\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/987da0d0-2366-47d6-aa25-904e24991866#fs-id1167829741770\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Solve for <em data-effect=\"italics\">y<\/em>: \\(y-3=-2\\left(x+1\\right).\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/b03538a1-8a7b-4158-a68b-e0e8a24c9fd4#fs-id1167835229496\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><\/ol><\/div><p>How do online companies know that \u201cyou may also like\u201d a particular item based on something you just ordered? How can economists know how a rise in the minimum wage will affect the unemployment rate? How do medical researchers create drugs to target cancer cells? How can traffic engineers predict the effect on your commuting time of an increase or decrease in gas prices? It\u2019s all mathematics.<\/p><p id=\"fs-id1167836300272\">The physical sciences, social sciences, and the business world are full of situations that can be modeled with linear equations relating two variables. To create a mathematical model of a linear relation between two variables, we must be able to find the equation of the line. In this section, we will look at several ways to write the equation of a line. The specific method we use will be determined by what information we are given.<\/p><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836601891\"><h3 data-type=\"title\">Find an Equation of the Line Given the Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/h3><p id=\"fs-id1167829650554\">We can easily determine the slope and intercept of a line if the equation is written in slope-intercept form, \\(y=mx+b.\\) Now we will do the reverse\u2014we will start with the slope and <em data-effect=\"italics\">y<\/em>-intercept and use them to find the equation of the line.<\/p><div data-type=\"example\" id=\"fs-id1167833054952\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836640431\"><div data-type=\"problem\" id=\"fs-id1167833021115\"><p id=\"fs-id1167836706728\">Find the equation of a line with slope \\(-9\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829717392\"><p id=\"fs-id1167829645042\">Since we are given the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line, we can substitute the needed values into the slope-intercept form, \\(y=mx+b.\\)<\/p><table id=\"fs-id1167836686077\" class=\"unnumbered unstyled\" summary=\"Name the slope. m equals negative 9. Name the y-intercept. The y-intercept is (0, negative 4). Substitute the values into y equals m x plus b. y equals negative 9 x plus negative 4. The m and negative 4 are both emphasized in red. The b and negative 4 are both emphasized in blue. This simplifies to y equals negative 9 x minus 4.\" data-label=\"\"><tbody><tr><td data-valign=\"top\" data-align=\"left\">Name the slope.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836341614\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td data-valign=\"top\" data-align=\"left\">Name the <em data-effect=\"italics\">y<\/em>-intercept.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td data-valign=\"top\" data-align=\"left\">Substitute the values into \\(y=mx+b.\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836615581\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829599074\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833050669\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836614830\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836730567\"><div data-type=\"problem\" id=\"fs-id1167833020885\"><p id=\"fs-id1167829905530\">Find the equation of a line with slope \\(\\frac{2}{5}\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836688878\"><p id=\"fs-id1167833365618\">\\(y=\\frac{2}{5}x+4\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829614246\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833257642\"><div data-type=\"problem\" id=\"fs-id1167836556216\"><p id=\"fs-id1167824652508\">Find the equation of a line with slope \\(-1\\) and <em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-3\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836692872\"><p id=\"fs-id1167836546955\">\\(y=\\text{\u2212}x-3\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836415102\">Sometimes, the slope and intercept need to be determined from the graph.<\/p><div data-type=\"example\" id=\"fs-id1167836450394\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167825091753\"><div data-type=\"problem\" id=\"fs-id1167836608164\"><p id=\"fs-id1167829597566\">Find the equation of the line shown in the graph.<\/p><span data-type=\"media\" id=\"fs-id1167830123714\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 3, negative 6), (0, negative 4), (3, negative 2), and (6, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_002_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 3, negative 6), (0, negative 4), (3, negative 2), and (6, 0).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836526766\"><p id=\"fs-id1167826130705\">We need to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line from the graph so we can substitute the needed values into the slope-intercept form, \\(y=mx+b.\\)<\/p><p id=\"fs-id1167833310695\">To find the slope, we choose two points on the graph.<\/p><p id=\"fs-id1167830077375\">The <em data-effect=\"italics\">y<\/em>-intercept is \\(\\left(0,-4\\right)\\) and the graph passes through \\(\\left(3,-2\\right).\\)<\/p><table id=\"fs-id1167829860698\" class=\"unnumbered unstyled\" summary=\"Find the slope, by counting the rise and run. m equals rise divided by run. m equals 2 divided by 3. Find the y-intercept. y-intercept is (0, negative 4). Substitute the values into y equals m x plus b. y equals 2 divided by 3 x minus 4. The m and 2 divided by 3 are both emphasized in red. The b and negative 4 are emphasized in blue.\" data-label=\"\"><tbody><tr><td data-valign=\"top\" data-align=\"left\">Find the slope, by counting the rise and run.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836615805\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829594439\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td data-valign=\"top\" data-align=\"left\">Find the <em data-effect=\"italics\">y<\/em>-intercept.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836560229\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td data-valign=\"top\" data-align=\"left\">Substitute the values into \\(y=mx+b.\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167826171770\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836513064\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836536600\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836318591\"><div data-type=\"problem\" id=\"fs-id1167836321281\"><p id=\"fs-id1167836628664\">Find the equation of the line shown in the graph.<\/p><span data-type=\"media\" id=\"fs-id1167824700008\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 5, negative 2), (0, 1), and (5, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_004_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 5, negative 2), (0, 1), and (5, 4).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167829690492\"><p id=\"fs-id1167836333597\">\\(y=\\frac{3}{5}x+1\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833056308\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836624567\"><div data-type=\"problem\" id=\"fs-id1167826025447\"><p id=\"fs-id1167829595577\">Find the equation of the line shown in the graph.<\/p><span data-type=\"media\" id=\"fs-id1167836607892\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 5), (3, negative 1), and (6, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_005_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 5), (3, negative 1), and (6, 3).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167824735214\"><p id=\"fs-id1167832956878\">\\(y=\\frac{4}{3}x-5\\)<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167829791300\"><h3 data-type=\"title\">Find an Equation of the Line Given the Slope and a Point<\/h3><p id=\"fs-id1167825913830\">Finding an equation of a line using the slope-intercept form of the equation works well when you are given the slope and <em data-effect=\"italics\">y<\/em>-intercept or when you read them off a graph. But what happens when you have another point instead of the <em data-effect=\"italics\">y<\/em>-intercept?<\/p><p id=\"fs-id1167836433751\">We are going to use the slope formula to derive another form of an equation of the line.<\/p><p id=\"fs-id1167836619863\">Suppose we have a line that has slope <em data-effect=\"italics\">m<\/em> and that contains some specific point \\(\\left({x}_{1},{y}_{1}\\right)\\) and some other point, which we will just call \\(\\left(x,y\\right).\\) We can write the slope of this line and then change it to a different form.<\/p><p id=\"fs-id1167829755664\">\\(\\begin{array}{cccccc}&amp; &amp; &amp; \\hfill m&amp; =\\hfill &amp; \\frac{y-{y}_{1}}{x-{x}_{1}}\\hfill \\\\ \\text{Multiply both sides of the equation by}\\phantom{\\rule{0.2em}{0ex}}x-{x}_{1}.\\hfill &amp; &amp; &amp; \\hfill m\\left(x-{x}_{1}\\right)&amp; =\\hfill &amp; \\left(\\frac{y-{y}_{1}}{x-{x}_{1}}\\right)\\left(x-{x}_{1}\\right)\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; \\hfill m\\left(x-{x}_{1}\\right)&amp; =\\hfill &amp; y-{y}_{1}\\hfill \\\\ \\text{Rewrite the equation with the}\\phantom{\\rule{0.2em}{0ex}}y\\phantom{\\rule{0.2em}{0ex}}\\text{terms on the left.}\\hfill &amp; &amp; &amp; \\hfill y-{y}_{1}&amp; =\\hfill &amp; m\\left(x-{x}_{1}\\right)\\hfill \\end{array}\\)<\/p><p id=\"fs-id1167833008035\">This format is called the <span data-type=\"term\">point-slope form<\/span> of an equation of a line.<\/p><div data-type=\"note\" id=\"fs-id1167824764782\"><div data-type=\"title\">Point-slope Form of an Equation of a Line<\/div><p id=\"fs-id1167829811866\">The <strong data-effect=\"bold\">point-slope form<\/strong> of an equation of a line with slope <em data-effect=\"italics\">m<\/em> and containing the point \\(\\left({x}_{1},{y}_{1}\\right)\\) is:<\/p><div data-type=\"equation\" id=\"fs-id1171792805591\" class=\"unnumbered\" data-label=\"\">\\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\)<\/div><\/div><p id=\"fs-id1167829936919\">We can use the point-slope form of an equation to find an equation of a line when we know the slope and at least one point. Then, we will rewrite the equation in slope-intercept form. Most applications of linear equations use the the slope-intercept form.<\/p><div data-type=\"example\" id=\"fs-id1167836554239\" class=\"textbox textbox--examples\"><div data-type=\"title\">How to Find an Equation of a Line Given a Point and the Slope<\/div><div data-type=\"exercise\" id=\"fs-id1167833379832\"><div data-type=\"problem\" id=\"fs-id1167826204850\"><p id=\"fs-id1167836600443\">Find an equation of a line with slope \\(m=-\\frac{1}{3}\\) that contains the point \\(\\left(6,-4\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836543755\"><span data-type=\"media\" id=\"fs-id1167832940173\" data-alt=\"Step 1 is to identify the slope. The slope is given. m equals negative 1 divided by 3.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_007a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to identify the slope. The slope is given. m equals negative 1 divided by 3.\"><\/span><span data-type=\"media\" id=\"fs-id1167826077317\" data-alt=\"Step 2 is to identify the point. The point is given. x 1 is 6 and y 1 is negative 4.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_007b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to identify the point. The point is given. x 1 is 6 and y 1 is negative 4.\"><\/span><span data-type=\"media\" id=\"fs-id1167832926786\" data-alt=\"Step 3 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 4 equals negative 1 divided by 3 times the quantity x minus 6 in parentheses. This simplifies to y plus 4 equals negative 1 divided by 3 times x plus 2.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_007c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 4 equals negative 1 divided by 3 times the quantity x minus 6 in parentheses. This simplifies to y plus 4 equals negative 1 divided by 3 times x plus 2.\"><\/span><span data-type=\"media\" id=\"fs-id1167836357296\" data-alt=\"Step 4 is to write the equation in slope-intercept form. y equals negative 1 divided by 3 times x minus 2.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_007d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to write the equation in slope-intercept form. y equals negative 1 divided by 3 times x minus 2.\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167826102710\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836789252\"><div data-type=\"problem\" id=\"fs-id1167826204767\"><p id=\"fs-id1167836728250\">Find the equation of a line with slope \\(m=-\\frac{2}{5}\\) and containing the point \\(\\left(10,-5\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829807832\"><p id=\"fs-id1167829860129\">\\(y=-\\frac{2}{5}x-1\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167832939589\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167832956627\"><div data-type=\"problem\" id=\"fs-id1167836800483\"><p id=\"fs-id1167836294992\">Find the equation of a line with slope \\(m=-\\frac{3}{4},\\) and containing the point \\(\\left(4,-7\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829627970\"><p id=\"fs-id1167833052972\">\\(y=-\\frac{3}{4}x-4\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167824704952\">We list the steps for easy reference.<\/p><div data-type=\"note\" id=\"fs-id1167826205373\" class=\"howto\"><div data-type=\"title\">To find an equation of a line given the slope and a point.<\/div><ol id=\"fs-id1167825011557\" type=\"1\" class=\"stepwise\"><li>Identify the slope.<\/li><li>Identify the point.<\/li><li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/li><li>Write the equation in slope-intercept form.<\/li><\/ol><\/div><div data-type=\"example\" id=\"fs-id1167836502652\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836607675\"><div data-type=\"problem\" id=\"fs-id1167833186433\"><p id=\"fs-id1167824976173\">Find an equation of a horizontal line that contains the point \\(\\left(-2,-6\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829784999\"><p id=\"fs-id1167833081974\">Every horizontal line has slope 0. We can substitute the slope and points into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/p><table id=\"fs-id1167833326479\" class=\"unnumbered unstyled\" summary=\"Identify the slope. m equals 0. Identify the point. x 1 is negative 2 and y 1 is negative 6. Substitute the values into y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 6 equals 0 times the quantity x minus negative 2 in parentheses. This simplifies to y plus 6 equals 0 or y equals negative 6. Write in slope-intercept form. It is in y-form, but could be written y equals 0 x minus 6. Did we end up with the form of a horizontal line y equals a?\" data-label=\"\"><tbody><tr><td data-valign=\"top\" data-align=\"left\">Identify the slope.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836689589\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td data-valign=\"top\" data-align=\"left\">Identify the point.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167824734208\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td data-valign=\"top\" data-align=\"left\">Substitute the values into \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836775057\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833329257\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833328934\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167822996903\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr><td data-valign=\"top\" data-align=\"left\">Write in slope-intercept form.<\/td><td data-valign=\"top\" data-align=\"left\">It is in <em data-effect=\"italics\">y<\/em>-form, but could be written \\(y=0x-6.\\)<\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167833025091\">Did we end up with the form of a horizontal line, \\(y=a?\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167824811964\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836509248\"><div data-type=\"problem\" id=\"fs-id1167833009418\"><p id=\"fs-id1167836356562\">Find the equation of a horizontal line containing the point \\(\\left(-3,8\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833377584\"><p id=\"fs-id1167829752219\">\\(y=8\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836409181\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833158283\"><div data-type=\"problem\" id=\"fs-id1167836312136\"><p id=\"fs-id1167829719636\">Find the equation of a horizontal line containing the point \\(\\left(-1,4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829595237\"><p id=\"fs-id1167836625469\">\\(y=4\\)<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836335402\"><h3 data-type=\"title\">Find an Equation of the Line Given Two Points<\/h3><p id=\"fs-id1167836398532\">When real-world data is collected, a linear model can be created from two data points. In the next example we\u2019ll see how to find an equation of a line when just two points are given.<\/p><p id=\"fs-id1167836595901\">So far, we have two options for finding an equation of a line: slope-intercept or point-slope. When we start with two points, it makes more sense to use the point-slope form.<\/p><p id=\"fs-id1167826130820\">But then we need the slope. Can we find the slope with just two points? Yes. Then, once we have the slope, we can use it and one of the given points to find the equation.<\/p><div data-type=\"example\" id=\"fs-id1167829715551\" class=\"textbox textbox--examples\"><div data-type=\"title\">How to Find the Equation of a Line Given Two Points<\/div><div data-type=\"exercise\" id=\"fs-id1167829893884\"><div data-type=\"problem\" id=\"fs-id1167823013300\"><p id=\"fs-id1167836329684\">Find an equation of a line that contains the points \\(\\left(-3,-1\\right)\\) and \\(\\left(2,-2\\right)\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836611614\"><span data-type=\"media\" id=\"fs-id1167829853073\" data-alt=\"Step 1 is to find the slope using the given points. Find the slope of the line through (negative 3, negative 1) and (2, and negative 2). m equals the quotient of y 2 minus y 1 in parentheses and x 2 minus x 1 in parentheses. m equals the quotient of negative 2 minus negative 1 in parentheses and 2 minus negative 3 in parentheses. m equals negative 1 divided by 5.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_009a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to find the slope using the given points. Find the slope of the line through (negative 3, negative 1) and (2, and negative 2). m equals the quotient of y 2 minus y 1 in parentheses and x 2 minus x 1 in parentheses. m equals the quotient of negative 2 minus negative 1 in parentheses and 2 minus negative 3 in parentheses. m equals negative 1 divided by 5.\"><\/span><span data-type=\"media\" id=\"fs-id1167829720040\" data-alt=\"Step 2 is to identify the point. Choose either point. x 1 is 2 and y 1 is negative 2.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_009b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to identify the point. Choose either point. x 1 is 2 and y 1 is negative 2.\"><\/span><span data-type=\"media\" id=\"fs-id1167825836127\" data-alt=\"Step 3 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 2 equals negative 1 divided by 5 times the quantity x minus 2 in parentheses. This simplifies to y plus 2 equals negative 1 divided by 5 times x plus 2 divided by 5.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_009c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 2 equals negative 1 divided by 5 times the quantity x minus 2 in parentheses. This simplifies to y plus 2 equals negative 1 divided by 5 times x plus 2 divided by 5.\"><\/span><span data-type=\"media\" id=\"fs-id1167829619192\" data-alt=\"Step 4 is to write the equation in slope-intercept form. y equals negative 1 divided by 5 times x minus 8 divided by 5.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_009d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to write the equation in slope-intercept form. y equals negative 1 divided by 5 times x minus 8 divided by 5.\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836534523\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836433959\"><div data-type=\"problem\" id=\"fs-id1167824653042\"><p id=\"fs-id1167823012200\">Find the equation of a line containing the points \\(\\left(-2,-4\\right)\\) and \\(\\left(1,-3\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829692284\"><p id=\"fs-id1167836415614\">\\(y=\\frac{1}{3}x-\\frac{10}{3}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836730055\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829893622\"><div data-type=\"problem\" id=\"fs-id1167836640506\"><p id=\"fs-id1167836683962\">Find the equation of a line containing the points \\(\\left(-4,-3\\right)\\) and \\(\\left(1,-5\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836575727\"><p id=\"fs-id1167833096636\">\\(y=-\\frac{2}{5}x-\\frac{23}{5}\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836433564\">The steps are summarized here.<\/p><div data-type=\"note\" id=\"fs-id1167836293926\" class=\"howto\"><div data-type=\"title\">To find an equation of a line given two points.<\/div><ol id=\"fs-id1167832980824\" type=\"1\" class=\"stepwise\"><li>Find the slope using the given points. \\(m=\\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\)<\/li><li>Choose one point.<\/li><li>Substitute the values into the point-slope form: \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/li><li>Write the equation in slope-intercept form.<\/li><\/ol><\/div><div data-type=\"example\" id=\"fs-id1167836596902\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833009830\"><div data-type=\"problem\"><p id=\"fs-id1167836544330\">Find an equation of a line that contains the points \\(\\left(-3,5\\right)\\) and \\(\\left(-3,4\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167836800401\">Again, the first step will be to find the slope.<\/p><p id=\"fs-id1167836283420\">\\(\\begin{array}{cccc}\\begin{array}{c}\\text{Find the slope of the line through}\\phantom{\\rule{0.2em}{0ex}}\\left(-3,5\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}\\left(-3,4\\right).\\hfill \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\end{array}\\hfill &amp; &amp; &amp; \\phantom{\\rule{1em}{0ex}}\\begin{array}{ccc}\\hfill m&amp; =\\hfill &amp; \\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\hfill \\\\ \\hfill m&amp; =\\hfill &amp; \\frac{4-5}{-3-\\left(-3\\right)}\\hfill \\\\ \\hfill m&amp; =\\hfill &amp; \\frac{-1}{0}\\hfill \\end{array}\\hfill \\\\ &amp; &amp; &amp; \\text{The slope is undefined.}\\hfill \\end{array}\\)<\/p><p id=\"fs-id1167833397134\">This tells us it is a vertical line. Both of our points have an <em data-effect=\"italics\">x<\/em>-coordinate of \\(-2.\\) So our equation of the line is \\(x=-2.\\) Since there is no <em data-effect=\"italics\">y<\/em>, we cannot write it in slope-intercept form.<\/p><p id=\"fs-id1167833381342\">You may want to sketch a graph using the two given points. Does your graph agree with our conclusion that this is a vertical line?<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836544022\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836520875\"><p id=\"fs-id1167836485974\">Find the equation of a line containing the points \\(\\left(5,1\\right)\\) and \\(\\left(5,-4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836701061\"><p id=\"fs-id1167829752657\">\\(x=5\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836532553\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836619179\"><div data-type=\"problem\" id=\"fs-id1167833407674\"><p id=\"fs-id1167836646048\">Find the equaion of a line containing the points \\(\\left(-4,4\\right)\\) and \\(\\left(-4,3\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833023052\"><p id=\"fs-id1167836289656\">\\(x=-4\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836614877\">We have seen that we can use either the slope-intercept form or the point-slope form to find an equation of a line. Which form we use will depend on the information we are given.<\/p><table id=\"fs-id1167836293795\" class=\"unnumbered\" summary=\"The table is titled To Write and Equation of a Line. It has three columns labeled \u201cIf given,\u201d \u201cUse,\u201d, and \u201cForm.\u201d The first row shows that if the slope and y intercept are given, use the slope-intercept form, which is y equals mx plus b. The second row shows that if the slope and a point are given, use the point-slope form, which is y minus y sub 1 equals m times the quantity x minus x sub 1.\"><thead><tr><th colspan=\"3\" data-valign=\"middle\" data-align=\"center\">To Write an Equation of a Line<\/th><\/tr><\/thead><tbody><tr><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">If given:<\/strong><\/td><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">Use:<\/strong><\/td><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">Form:<\/strong><\/td><\/tr><tr><td data-valign=\"middle\" data-align=\"left\">Slope and <em data-effect=\"italics\">y<\/em>-intercept<\/td><td data-valign=\"middle\" data-align=\"left\">slope-intercept<\/td><td data-valign=\"middle\" data-align=\"left\">\\(y=mx+b\\)<\/td><\/tr><tr><td data-valign=\"middle\" data-align=\"left\">Slope and a point<\/td><td data-valign=\"middle\" data-align=\"left\">point-slope<\/td><td data-valign=\"middle\" data-align=\"left\">\\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\)<\/td><\/tr><tr><td data-valign=\"middle\" data-align=\"left\">Two points<\/td><td data-valign=\"middle\" data-align=\"left\">point-slope<\/td><td data-valign=\"middle\" data-align=\"left\">\\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\)<\/td><\/tr><\/tbody><\/table><\/div><div class=\"bc-section section\" data-depth=\"1\"><h3 data-type=\"title\">Find an Equation of a Line Parallel to a Given Line<\/h3><p id=\"fs-id1167833047491\">Suppose we need to find an equation of a line that passes through a specific point and is parallel to a given line. We can use the fact that parallel lines have the same slope. So we will have a point and the slope\u2014just what we need to use the point-slope equation.<\/p><p id=\"fs-id1167836312500\">First, let\u2019s look at this graphically.<\/p><p id=\"fs-id1167829716102\">This graph shows \\(y=2x-3.\\) We want to graph a line parallel to this line and passing through the point \\(\\left(-2,1\\right).\\)<\/p><span data-type=\"media\" id=\"fs-id1167836320481\" data-alt=\"This figure has a graph of a straight line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The point (negative 2, 1) is plotted. The line does not go through the point (negative 2, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_010_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The point (negative 2, 1) is plotted. The line does not go through the point (negative 2, 1).\"><\/span><p id=\"fs-id1167836697298\">We know that parallel lines have the same slope. So the second line will have the same slope as \\(y=2x-3.\\) That slope is \\({m}_{\\parallel }=2.\\) We\u2019ll use the notation \\({m}_{\\parallel }\\) to represent the slope of a line parallel to a line with slope <em data-effect=\"italics\">m<\/em>. (Notice that the subscript || looks like two parallel lines.)<\/p><p id=\"fs-id1167829743890\">The second line will pass through \\(\\left(-2,1\\right)\\) and have \\(m=2.\\)<\/p><p id=\"fs-id1167836289727\">To graph the line, we start at\\(\\left(-2,1\\right)\\) and count out the rise and run.<\/p><p id=\"fs-id1167836700923\">With \\(m=2\\) (or \\(m=\\frac{2}{1}\\)), we count out the rise 2 and the run 1. We draw the line, as shown in the graph.<\/p><span data-type=\"media\" id=\"fs-id1167829713321\" data-alt=\"This figure has a graph of a two straight lines on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The first line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The points (negative 2, 1) and (negative 1, 3) are plotted. The second line goes through the points (negative 2, 1) and (negative 1, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_011_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a two straight lines on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The first line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The points (negative 2, 1) and (negative 1, 3) are plotted. The second line goes through the points (negative 2, 1) and (negative 1, 3).\"><\/span><p id=\"fs-id1167829696351\">Do the lines appear parallel? Does the second line pass through\\(\\left(-2,1\\right)?\\)<\/p><p id=\"fs-id1167836305436\">We were asked to graph the line, now let\u2019s see how to do this algebraically.<\/p><p id=\"fs-id1167836493048\">We can use either the slope-intercept form or the point-slope form to find an equation of a line. Here we know one point and can find the slope. So we will use the point-slope form.<\/p><div data-type=\"example\" id=\"fs-id1167836300038\" class=\"textbox textbox--examples\"><div data-type=\"title\">How to Find the Equation of a Line Parallel to a Given Line and a Point<\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836410330\"><p id=\"fs-id1167836596689\">Find an equation of a line parallel to \\(y=2x-3\\) that contains the point \\(\\left(-2,1\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836623976\"><span data-type=\"media\" id=\"fs-id1167836686744\" data-alt=\"Step 1 is to find the slope of the given line. The line is in slope-intercept form, y equals 2 x minus 3. m equals 2.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to find the slope of the given line. The line is in slope-intercept form, y equals 2 x minus 3. m equals 2.\"><\/span><span data-type=\"media\" id=\"fs-id1167836508752\" data-alt=\"Step 2 is to find the slope of the parallel line. Parallel lines have the same slope. m equals 2.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to find the slope of the parallel line. Parallel lines have the same slope. m equals 2.\"><\/span><span data-type=\"media\" id=\"fs-id1167836313488\" data-alt=\"Step 3 is to identify the point. The given point is (negative 2, 1). x 1 is negative 2 and y 1 is 1.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to identify the point. The given point is (negative 2, 1). x 1 is negative 2 and y 1 is 1.\"><\/span><span data-type=\"media\" id=\"fs-id1167829596586\" data-alt=\"Step 4 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus 1 equals 2 times the quantity x minus negative 2 in parentheses. This simplifies to y minus 1 equals 2 x plus 4.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus 1 equals 2 times the quantity x minus negative 2 in parentheses. This simplifies to y minus 1 equals 2 x plus 4.\"><\/span><span data-type=\"media\" id=\"fs-id1167836635332\" data-alt=\"Step 5 is to write the equation in slope-intercept form. y equals 2 x plus 5.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012e_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 5 is to write the equation in slope-intercept form. y equals 2 x plus 5.\"><\/span><p id=\"fs-id1167833061296\">Look at graph with the parallel lines shown previously. Does this equation make sense? What is the <em data-effect=\"italics\">y<\/em>-intercept of the line? What is the slope?<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836580165\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836611133\"><div data-type=\"problem\" id=\"fs-id1167829894247\"><p id=\"fs-id1167829683684\">Find an equation of a line parallel to the line \\(y=3x+1\\) that contains the point \\(\\left(4,2\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167825660367\"><p>\\(y=3x-10\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167832999699\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836628180\"><div data-type=\"problem\" id=\"fs-id1167833224723\"><p id=\"fs-id1167824732116\">Find an equation of a line parallel to the line \\(y=\\frac{1}{2}x-3\\) that contains the point \\(\\left(6,4\\right).\\)<\/p><p>Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836289214\"><p id=\"fs-id1167836538340\">\\(y=\\frac{1}{2}x+1\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" class=\"howto\"><div data-type=\"title\">Find an equation of a line parallel to a given line.<\/div><ol id=\"fs-id1167829879306\" type=\"1\" class=\"stepwise\"><li>Find the slope of the given line.<\/li><li>Find the slope of the parallel line.<\/li><li>Identify the point.<\/li><li>Substitute the values into the point-slope form: \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/li><li>Write the equation in slope-intercept form.<\/li><\/ol><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836513856\"><h3 data-type=\"title\">Find an Equation of a Line Perpendicular to a Given Line<\/h3><p id=\"fs-id1167826204724\">Now, let\u2019s consider perpendicular lines. Suppose we need to find a line passing through a specific point and which is perpendicular to a given line. We can use the fact that perpendicular lines have slopes that are negative reciprocals. We will again use the point-slope equation, like we did with parallel lines.<\/p><p id=\"fs-id1167829834014\">This graph shows \\(y=2x-3.\\) Now, we want to graph a line perpendicular to this line and passing through \\(\\left(-2,1\\right).\\)<\/p><span data-type=\"media\" id=\"fs-id1167829578789\" data-alt=\"This figure has a graph of a straight line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The point (negative 2, 1) is plotted. The line does not go through the point (negative 2, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The point (negative 2, 1) is plotted. The line does not go through the point (negative 2, 1).\"><\/span><p id=\"fs-id1167836534688\">We know that perpendicular lines have slopes that are negative reciprocals.<\/p><p id=\"fs-id1167836553112\">We\u2019ll use the notation \\({m}_{\\perp }\\) to represent the slope of a line perpendicular to a line with slope <em data-effect=\"italics\">m<\/em>. (Notice that the subscript \\(\\perp \\) looks like the right angles made by two perpendicular lines.)<\/p><div data-type=\"equation\" id=\"fs-id1167833022890\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{cccc}y=2x-3\\hfill &amp; &amp; &amp; \\text{perpendicular line}\\hfill \\\\ m=2\\hfill &amp; &amp; &amp; {m}_{\\perp }=-\\frac{1}{2}\\hfill \\end{array}\\)<\/div><p id=\"fs-id1167836575849\">We now know the perpendicular line will pass through \\(\\left(-2,1\\right)\\) with \\({m}_{\\perp }=-\\frac{1}{2}.\\)<\/p><p id=\"fs-id1167829627541\">To graph the line, we will start at \\(\\left(-2,1\\right)\\) and count out the rise \\(-1\\) and the run 2. Then we draw the line.<\/p><span data-type=\"media\" id=\"fs-id1167830095268\" data-alt=\"This figure has a graph of two perpendicular straight lines on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The first line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The points (negative 2, 1) and (0, 0) are plotted. A right triangle is drawn connecting the points (negative 2, 1), (negative 2, 0), and (0, 0). The second line goes through the points (negative 2, 1) and (0, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_013_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of two perpendicular straight lines on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The first line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The points (negative 2, 1) and (0, 0) are plotted. A right triangle is drawn connecting the points (negative 2, 1), (negative 2, 0), and (0, 0). The second line goes through the points (negative 2, 1) and (0, 0).\"><\/span><p id=\"fs-id1167836296407\">Do the lines appear perpendicular? Does the second line pass through\\(\\left(-2,1\\right)?\\)<\/p><p id=\"fs-id1167829627933\">We were asked to graph the line, now, let\u2019s see how to do this algebraically.<\/p><p id=\"fs-id1167825703151\">We can use either the slope-intercept form or the point-slope form to find an equation of a line. In this example we know one point, and can find the slope, so we will use the point-slope form.<\/p><div data-type=\"example\" id=\"fs-id1167829737780\" class=\"textbox textbox--examples\"><div data-type=\"title\">How to Find the Equation of a Line Perpendicular to a Given Line and a Point<\/div><div data-type=\"exercise\" id=\"fs-id1167833338703\"><div data-type=\"problem\" id=\"fs-id1167836570858\"><p id=\"fs-id1167836790223\">Find an equation of a line perpendicular to \\(y=2x-3\\) that contains the point \\(\\left(-2,1\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836539459\"><span data-type=\"media\" id=\"fs-id1167836527833\" data-alt=\"Step 1 is to find the slope of the given line. The line is in slope-intercept form, y equals 2 x minus 3. m equals 2.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to find the slope of the given line. The line is in slope-intercept form, y equals 2 x minus 3. m equals 2.\"><\/span><span data-type=\"media\" id=\"fs-id1167836286660\" data-alt=\"Step 2 is to find the slope of the perpendicular line. The slopes of perpendicular lines are negative reciprocals. m equals negative 1 divided by 2\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to find the slope of the perpendicular line. The slopes of perpendicular lines are negative reciprocals. m equals negative 1 divided by 2\"><\/span><span data-type=\"media\" id=\"fs-id1167836731058\" data-alt=\"Step 3 is to identify the point. The given point is (negative 2, 1). x 1 is negative 2 and y 1 is 1.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to identify the point. The given point is (negative 2, 1). x 1 is negative 2 and y 1 is 1.\"><\/span><span data-type=\"media\" id=\"fs-id1167832940562\" data-alt=\"Step 4 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus 1 equals negative 1 divided by 2 times the quantity x minus negative 2 in parentheses. This simplifies to y minus 1 equals negative 1 divided by 2 times the quantity x plus 2 in parentheses. This further simplifies to y minus 1 equals negative 1 divided by 2 times x minus 1.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus 1 equals negative 1 divided by 2 times the quantity x minus negative 2 in parentheses. This simplifies to y minus 1 equals negative 1 divided by 2 times the quantity x plus 2 in parentheses. This further simplifies to y minus 1 equals negative 1 divided by 2 times x minus 1.\"><\/span><span data-type=\"media\" id=\"fs-id1167836321997\" data-alt=\"Step 5 is to write the equation in slope-intercept form. y equals negative 1 divided by 2 times x.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014e_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 5 is to write the equation in slope-intercept form. y equals negative 1 divided by 2 times x.\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836510503\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833364838\"><div data-type=\"problem\" id=\"fs-id1167836615040\"><p id=\"fs-id1167836399749\">Find an equation of a line perpendicular to the line \\(y=3x+1\\) that contains the point \\(\\left(4,2\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167830093016\"><p id=\"fs-id1167832940087\">\\(y=-\\frac{1}{3}x+\\frac{10}{3}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829739244\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167832930300\"><div data-type=\"problem\" id=\"fs-id1167836390247\"><p id=\"fs-id1167836790119\">Find an equation of a line perpendicular to the line \\(y=\\frac{1}{2}x-3\\) that contains the point \\(\\left(6,4\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167829590431\">\\(y=-2x+16\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836513068\" class=\"howto\"><div data-type=\"title\">Find an equation of a line perpendicular to a given line.<\/div><ol id=\"fs-id1167833369074\" type=\"1\" class=\"stepwise\"><li>Find the slope of the given line.<\/li><li>Find the slope of the perpendicular line.<\/li><li>Identify the point.<\/li><li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/li><li>Write the equation in slope-intercept form.<\/li><\/ol><\/div><div data-type=\"example\" id=\"fs-id1167833061157\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833382937\"><div data-type=\"problem\" id=\"fs-id1167836329294\"><p id=\"fs-id1167836630433\">Find an equation of a line perpendicular to \\(x=5\\) that contains the point \\(\\left(3,-2\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836340178\"><p id=\"fs-id1167836549844\">Again, since we know one point, the point-slope option seems more promising than the slope-intercept option. We need the slope to use this form, and we know the new line will be perpendicular to \\(x=5.\\) This line is vertical, so its perpendicular will be horizontal. This tells us the \\({m}_{\\perp }=0.\\)<\/p><p id=\"fs-id1167836520781\">\\(\\begin{array}{cccc}\\text{Identify the point.}\\hfill &amp; &amp; &amp; \\hfill \\left(3,-2\\right)\\hfill \\\\ \\begin{array}{c}\\text{Identify the slope of the perpendicular line.}\\hfill \\\\ \\text{Substitute the values into}\\phantom{\\rule{0.2em}{0ex}}y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\hfill \\\\ \\\\ \\\\ \\\\ \\text{Simplify.}\\hfill \\\\ \\\\ \\\\ \\end{array}\\hfill &amp; &amp; &amp; \\hfill \\begin{array}{ccc}\\hfill {m}_{\\perp }&amp; =\\hfill &amp; 0\\hfill \\\\ \\hfill y-{y}_{1}&amp; =\\hfill &amp; m\\left(x-{x}_{1}\\right)\\hfill \\\\ \\hfill y-\\left(-2\\right)&amp; =\\hfill &amp; 0\\left(x-3\\right)\\hfill \\\\ \\hfill y+2&amp; =\\hfill &amp; 0\\hfill \\\\ \\hfill y&amp; =\\hfill &amp; -2\\hfill \\end{array}\\hfill \\end{array}\\)<\/p><p id=\"fs-id1167836533799\">Sketch the graph of both lines. On your graph, do the lines appear to be perpendicular?<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836520482\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829750618\"><div data-type=\"problem\" id=\"fs-id1167833274749\"><p id=\"fs-id1167836429672\">Find an equation of a line that is perpendicular to the line \\(x=4\\) that contains the point \\(\\left(4,-5\\right).\\). Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836486854\"><p id=\"fs-id1167836433816\">\\(y=-5\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833020343\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167829628068\"><p id=\"fs-id1167836701558\">Find an equation of a line that is perpendicular to the line \\(x=2\\) that contains the point \\(\\left(2,-1\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829594832\"><p id=\"fs-id1167832935722\">\\(y=-1\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167829789981\">In <a href=\"#fs-id1167833061157\" class=\"autogenerated-content\">(Figure)<\/a>, we used the point-slope form to find the equation. We could have looked at this in a different way.<\/p><p id=\"fs-id1167836539730\">We want to find a line that is perpendicular to \\(x=5\\) that contains the point \\(\\left(3,-2\\right).\\) This graph shows us the line\\(x=5\\) and the point \\(\\left(3,-2\\right).\\)<\/p><span data-type=\"media\" data-alt=\"This figure has a graph of a straight vertical line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (5, 0), (5, 1), and (5, 2). The point (3, negative 2) is plotted. The line does not go through the point (3, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_015_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight vertical line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (5, 0), (5, 1), and (5, 2). The point (3, negative 2) is plotted. The line does not go through the point (3, negative 2).\"><\/span><p id=\"fs-id1167826206025\">We know every line perpendicular to a vertical line is horizontal, so we will sketch the horizontal line through \\(\\left(3,-2\\right).\\)<\/p><span data-type=\"media\" data-alt=\"This figure has a graph of a straight vertical line and a straight horizontal line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The vertical line goes through the points (5, 0), (5, 1), and (5, 2). The horizontal line goes through the points (negative 2, negative 2), (0, negative 2), (3, negative 2), and (6, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_016_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight vertical line and a straight horizontal line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The vertical line goes through the points (5, 0), (5, 1), and (5, 2). The horizontal line goes through the points (negative 2, negative 2), (0, negative 2), (3, negative 2), and (6, negative 2).\"><\/span><p id=\"fs-id1167829690001\">Do the lines appear perpendicular?<\/p><p id=\"fs-id1167836418683\">If we look at a few points on this horizontal line, we notice they all have <em data-effect=\"italics\">y<\/em>-coordinates of \\(-2.\\) So, the equation of the line perpendicular to the vertical line \\(x=5\\) is \\(y=-2.\\)<\/p><div data-type=\"example\" id=\"fs-id1167836554451\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833257675\"><div data-type=\"problem\" id=\"fs-id1167829807866\"><p id=\"fs-id1167829743413\">Find an equation of a line that is perpendicular to \\(y=-3\\) that contains the point \\(\\left(-3,5\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167824651086\"><p id=\"fs-id1167829812775\">The line \\(y=-3\\) is a horizontal line. Any line perpendicular to it must be vertical, in the form \\(x=a.\\) Since the perpendicular line is vertical and passes through \\(\\left(-3,5\\right),\\) every point on it has an <em data-effect=\"italics\">x<\/em>-coordinate of \\(-3.\\) The equation of the perpendicular line is \\(x=-3\\)<\/p><p id=\"fs-id1167833020048\">You may want to sketch the lines. Do they appear perpendicular?<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836610994\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836310492\"><div data-type=\"problem\" id=\"fs-id1167836415129\"><p id=\"fs-id1167836700045\">Find an equation of a line that is perpendicular to the line \\(y=1\\) that contains the point \\(\\left(-5,1\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833379801\"><p id=\"fs-id1167836515773\">\\(x=-5\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829786398\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836594788\"><div data-type=\"problem\" id=\"fs-id1167826205784\"><p id=\"fs-id1167829691675\">Find an equation of a line that is perpendicular to the line \\(y=-5\\) that contains the point \\(\\left(-4,-5\\right).\\) Write the equation in slope-intercept form.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829748611\"><p id=\"fs-id1167836612514\">\\(x=-4\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833202337\" class=\"media-2\"><p id=\"fs-id1167836554915\">Access these online resources for additional instruction and practice with finding the equation of a line.<\/p><ul id=\"fs-id1167836558410\" data-display=\"block\"><li><a href=\"https:\/\/openstax.org\/l\/37slopeycept\">Write an Equation of Line Given its slope and Y-Intercept<\/a><\/li><li><a href=\"https:\/\/openstax.org\/l\/37slopepoint\">Using Point Slope Form to Write the Equation of a Line, Find the equation given slope and point<\/a><\/li><li><a href=\"https:\/\/openstax.org\/l\/37twoptspline\">Find the equation given two points<\/a><\/li><li><a href=\"https:\/\/openstax.org\/l\/37perpenpara\">Find the equation of perpendicular and parallel lines<\/a><\/li><\/ul><\/div><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836539487\"><h3 data-type=\"title\">Key Concepts<\/h3><ul id=\"fs-id1167833290521\" data-bullet-style=\"bullet\"><li><strong data-effect=\"bold\">How to find an equation of a line given the slope and a point.<\/strong><ol id=\"fs-id1167829746878\" type=\"1\" class=\"stepwise\"><li>Identify the slope.<\/li><li>Identify the point.<\/li><li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/li><li>Write the equation in slope-intercept form.<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><\/li><\/ol><\/li><li><strong data-effect=\"bold\">How to find an equation of a line given two points.<\/strong><ol id=\"fs-id1167836516510\" type=\"1\" class=\"stepwise\"><li>Find the slope using the given points. \\(m=\\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\)<\/li><li>Choose one point.<\/li><li>Substitute the values into the point-slope form: \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/li><li>Write the equation in slope-intercept form.<div data-type=\"newline\"><br><\/div> <table id=\"fs-id1167829579861\" class=\"unnumbered\" summary=\"The table is titled To Write and Equation of a Line. It has three columns labeled \u201cIf given,\u201d \u201cUse,\u201d, and \u201cForm.\u201d The first row shows that if the slope and y intercept are given, use the slope-intercept form, which is y equals mx plus b. The second row shows that if the slope and a point are given, use the point-slope form, which is y minus y sub 1 equals m times the quantity x minus x sub 1.\"><thead><tr><th colspan=\"3\" data-valign=\"middle\" data-align=\"center\">To Write an Equation of a Line<\/th><\/tr><\/thead><tbody><tr><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">If given:<\/strong><\/td><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">Use:<\/strong><\/td><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">Form:<\/strong><\/td><\/tr><tr><td data-valign=\"middle\" data-align=\"left\">Slope and <em data-effect=\"italics\">y<\/em>-intercept<\/td><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">slope-intercept<\/strong><\/td><td data-valign=\"middle\" data-align=\"left\">\\(y=mx+b\\)<\/td><\/tr><tr><td data-valign=\"middle\" data-align=\"left\">Slope and a point<\/td><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">point-slope<\/strong><\/td><td data-valign=\"middle\" data-align=\"left\">\\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\)<\/td><\/tr><tr><td data-valign=\"middle\" data-align=\"left\">Two points<\/td><td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">point-slope<\/strong><\/td><td data-valign=\"middle\" data-align=\"left\">\\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\)<\/td><\/tr><\/tbody><\/table><\/li><\/ol><\/li><li><strong data-effect=\"bold\">How to find an equation of a line parallel to a given line.<\/strong><ol id=\"fs-id1167836325992\" type=\"1\" class=\"stepwise\"><li>Find the slope of the given line.<\/li><li>Find the slope of the parallel line.<\/li><li>Identify the point.<\/li><li>Substitute the values into the point-slope form: \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/li><li>Write the equation in slope-intercept form<\/li><\/ol><\/li><li><strong data-effect=\"bold\">How to find an equation of a line perpendicular to a given line.<\/strong><ol id=\"fs-id1167836287222\" type=\"1\" class=\"stepwise\"><li>Find the slope of the given line.<\/li><li>Find the slope of the perpendicular line.<\/li><li>Identify the point.<\/li><li>Substitute the values into the point-slope form, \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right)\\)<\/li><li>Write the equation in slope-intercept form.<\/li><\/ol><\/li><\/ul><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836706806\"><div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167829589591\"><h4 data-type=\"title\">Practice Makes Perfect<\/h4><p id=\"fs-id1167836715608\"><strong data-effect=\"bold\">Find an Equation of the Line Given the Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/strong><\/p><p id=\"fs-id1167836415908\">In the following exercises, find the equation of a line with given slope and <em data-effect=\"italics\">y<\/em>-intercept. Write the equation in slope-intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167829753548\"><div data-type=\"problem\" id=\"fs-id1167829714595\"><p id=\"fs-id1167836319403\">slope 3 and<\/p><div data-type=\"newline\"><br><\/div>\\(y\\)-intercept \\(\\left(0,5\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167829695346\"><p id=\"fs-id1167829749967\">\\(y=3x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826097524\"><div data-type=\"problem\" id=\"fs-id1167833051126\"><p id=\"fs-id1167833240421\">slope 8 and<\/p><div data-type=\"newline\"><br><\/div><em data-effect=\"italics\">y<\/em>-intercept \\(\\left(0,-6\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829579132\"><div data-type=\"problem\" id=\"fs-id1167826205064\"><p id=\"fs-id1167833310065\">slope \\(-3\\) and<\/p><div data-type=\"newline\"><br><\/div>\\(y\\)-intercept \\(\\left(0,-1\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833379389\"><p id=\"fs-id1167836558333\">\\(y=-3x-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829810647\"><div data-type=\"problem\" id=\"fs-id1167829906500\"><p id=\"fs-id1167836547898\">slope \\(-1\\) and<\/p><div data-type=\"newline\"><br><\/div>\\(y\\)-intercept \\(\\left(0,3\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836387436\"><div data-type=\"problem\" id=\"fs-id1167836349166\"><p id=\"fs-id1167833056712\">slope \\(\\frac{1}{5}\\) and<\/p><div data-type=\"newline\"><br><\/div>\\(y\\)-intercept \\(\\left(0,-5\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836551668\"><p id=\"fs-id1167829715758\">\\(y=\\frac{1}{5}x-5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824767097\"><div data-type=\"problem\"><p id=\"fs-id1167836561278\">slope \\(-\\frac{3}{4}\\) and<\/p><div data-type=\"newline\"><br><\/div>\\(y\\)-intercept \\(\\left(0,-2\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829712261\"><div data-type=\"problem\" id=\"fs-id1167836447386\"><p id=\"fs-id1167836626157\">slope 0 and<\/p><div data-type=\"newline\"><br><\/div>\\(y\\)-intercept \\(\\left(0,-1\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836456484\"><p id=\"fs-id1167836287662\">\\(y=-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829711770\"><div data-type=\"problem\" id=\"fs-id1167836432947\"><p id=\"fs-id1167829921553\">slope \\(-4\\) and<\/p><div data-type=\"newline\"><br><\/div>\\(y\\)-intercept \\(\\left(0,0\\right)\\)<\/div><\/div><p id=\"fs-id1167833059421\">In the following exercises, find the equation of the line shown in each graph. Write the equation in slope-intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167836544522\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836626384\"><p id=\"fs-id1167833271997\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833271998\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 5), (1, negative 2), and (2, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_201_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 5), (1, negative 2), and (2, 1).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167829598941\"><p id=\"fs-id1167829853948\">\\(y=3x-5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833349591\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836507156\"><p id=\"fs-id1167836288754\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836288755\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 4), (1, 2), and (2, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_202_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 4), (1, 2), and (2, 0).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836440491\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829580573\"><p id=\"fs-id1167824839801\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167824839802\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (2, negative 2), and (6, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_203_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (2, negative 2), and (6, 0).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836550635\"><p id=\"fs-id1167836607064\">\\(y=\\frac{1}{2}x-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833361650\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167832936934\"><p id=\"fs-id1167833256684\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836520071\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (4, 5), and (8, 8).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_204_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (4, 5), and (8, 8).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836417359\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833128976\"><p id=\"fs-id1167833018360\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833018362\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 3), (3, negative 1), and (6, negative 5).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_205_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 3), (3, negative 1), and (6, negative 5).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167826177601\"><p id=\"fs-id1167836613599\">\\(y=-\\frac{4}{3}x+3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836485683\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829597028\"><p id=\"fs-id1167832927168\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833050769\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 1), (2, negative 4), and (4, negative 7).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_206_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 1), (2, negative 4), and (4, negative 7).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833274590\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829811991\"><p><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836321761\" data-alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_207_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167829754778\"><p id=\"fs-id1167836429456\">\\(y=-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836609306\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167832976669\"><p id=\"fs-id1167833339044\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833339046\" data-alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 6), (1, 6), and (2, 6).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_208_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 6), (1, 6), and (2, 6).\"><\/span><\/div><\/div><p id=\"fs-id1167836529707\"><strong data-effect=\"bold\">Find an Equation of the Line Given the Slope and a Point<\/strong><\/p><p id=\"fs-id1167833380664\">In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167833407507\"><div data-type=\"problem\" id=\"fs-id1167836731148\"><p id=\"fs-id1167829681166\">\\(m=\\frac{5}{8},\\) point \\(\\left(8,3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829783810\"><p id=\"fs-id1167836558580\">\\(y=\\frac{5}{8}x-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833047536\"><div data-type=\"problem\" id=\"fs-id1167836615924\"><p id=\"fs-id1167836792953\">\\(m=\\frac{5}{6},\\) point \\(\\left(6,7\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836509627\"><div data-type=\"problem\" id=\"fs-id1167829594543\"><p id=\"fs-id1167824737321\">\\(m=-\\frac{3}{5},\\) point \\(\\left(10,-5\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829720125\"><p id=\"fs-id1167836688498\">\\(y=-\\frac{3}{5}x+1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829811645\"><div data-type=\"problem\" id=\"fs-id1167836363112\"><p id=\"fs-id1167829751544\">\\(m=-\\frac{3}{4},\\) point \\(\\left(8,-5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826077523\"><div data-type=\"problem\" id=\"fs-id1167829749598\"><p id=\"fs-id1167829689340\">\\(m=-\\frac{3}{2},\\) point \\(\\left(-4,-3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829599864\"><p id=\"fs-id1167836561099\">\\(y=-\\frac{3}{2}x+9\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836699450\"><div data-type=\"problem\" id=\"fs-id1167824732204\"><p id=\"fs-id1167824773429\">\\(m=-\\frac{5}{2},\\) point \\(\\left(-8,-2\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833269887\"><div data-type=\"problem\" id=\"fs-id1167836729979\"><p id=\"fs-id1167836729981\">\\(m=-7,\\) point \\(\\left(-1,-3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836610073\"><p id=\"fs-id1167836610075\">\\(y=-7x-10\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833056175\"><div data-type=\"problem\" id=\"fs-id1167836510358\"><p id=\"fs-id1167836576450\">\\(m=-4,\\) point \\(\\left(-2,-3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829597969\"><div data-type=\"problem\" id=\"fs-id1167829597972\"><p id=\"fs-id1167836567138\">Horizontal line containing \\(\\left(-2,5\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829754568\"><p id=\"fs-id1167829785045\">\\(y=5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836495293\"><div data-type=\"problem\" id=\"fs-id1167836495295\"><p id=\"fs-id1167829620386\">Horizontal line containing \\(\\left(-2,-3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826083425\"><div data-type=\"problem\" id=\"fs-id1167826083427\"><p id=\"fs-id1167829905739\">Horizontal line containing \\(\\left(-1,-7\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833379180\"><p id=\"fs-id1167836602221\">\\(y=-7\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829620802\"><div data-type=\"problem\" id=\"fs-id1167829620804\"><p id=\"fs-id1167824740609\">Horizontal line containing \\(\\left(4,-8\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167833303310\"><strong data-effect=\"bold\">Find an Equation of the Line Given Two Points<\/strong><\/p><p id=\"fs-id1167829651567\">In the following exercises, find the equation of a line containing the given points. Write the equation in slope-intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167829880329\"><div data-type=\"problem\" id=\"fs-id1167829880331\"><p id=\"fs-id1167836518535\">\\(\\left(2,6\\right)\\) and \\(\\left(5,3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836543899\"><p id=\"fs-id1167836543902\">\\(y=\\text{\u2212}x+8\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832940554\"><div data-type=\"problem\" id=\"fs-id1167829691245\"><p id=\"fs-id1167836689328\">\\(\\left(4,3\\right)\\) and \\(\\left(8,1\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836526101\"><div data-type=\"problem\" id=\"fs-id1167836526103\"><p id=\"fs-id1167836792213\">\\(\\left(-3,-4\\right)\\) and \\(\\left(5-2\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836292965\"><p id=\"fs-id1167829595244\">\\(y=\\frac{1}{4}x-\\frac{13}{4}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829597670\"><div data-type=\"problem\" id=\"fs-id1167833356319\"><p id=\"fs-id1167833329138\">\\(\\left(-5,-3\\right)\\) and \\(\\left(4,-6\\right).\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833311141\"><div data-type=\"problem\" id=\"fs-id1167833311143\"><p id=\"fs-id1167836415243\">\\(\\left(-1,3\\right)\\) and \\(\\left(-6,-7\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829756066\"><p id=\"fs-id1167824764624\">\\(y=2x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829726391\"><div data-type=\"problem\" id=\"fs-id1167832982215\"><p id=\"fs-id1167832982217\">\\(\\left(-2,8\\right)\\) and \\(\\left(-4,-6\\right).\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833009732\"><div data-type=\"problem\" id=\"fs-id1167829753956\"><p id=\"fs-id1167836506442\">\\(\\left(0,4\\right)\\) and \\(\\left(2,-3\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167824617257\"><p id=\"fs-id1167833076770\">\\(y=-\\frac{7}{2}x+4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824737272\"><div data-type=\"problem\" id=\"fs-id1167836434306\"><p id=\"fs-id1167829786961\">\\(\\left(0,-2\\right)\\) and \\(\\left(-5,-3\\right).\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836524732\"><div data-type=\"problem\" id=\"fs-id1167836524735\"><p id=\"fs-id1167825702449\">\\(\\left(7,2\\right)\\) and \\(\\left(7,-2\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826131285\"><p id=\"fs-id1167826131287\">\\(x=7\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836322984\"><div data-type=\"problem\" id=\"fs-id1167836418558\"><p id=\"fs-id1167836418560\">\\(\\left(-2,1\\right)\\) and \\(\\left(-2,-4\\right).\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829894553\"><div data-type=\"problem\" id=\"fs-id1167826206606\"><p id=\"fs-id1167826206608\">\\(\\left(3,-4\\right)\\) and \\(\\left(5,-4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167824607152\"><p id=\"fs-id1167824607154\">\\(y=-4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824590416\"><div data-type=\"problem\" id=\"fs-id1167833309132\"><p id=\"fs-id1167833309135\">\\(\\left(-6,-3\\right)\\) and \\(\\left(-1,-3\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167836756855\"><strong data-effect=\"bold\">Find an Equation of a Line Parallel to a Given Line<\/strong><\/p><p id=\"fs-id1167836738196\">In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167836567374\"><div data-type=\"problem\" id=\"fs-id1167829893821\"><p id=\"fs-id1167829893823\">line \\(y=4x+2,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(1,2\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167832945777\"><p id=\"fs-id1167833272217\">\\(y=4x-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836598894\"><div data-type=\"problem\" id=\"fs-id1167829741274\"><p id=\"fs-id1167829741276\">line \\(y=-3x-1,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(2,-3\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836787998\"><div data-type=\"problem\" id=\"fs-id1167829810536\"><p id=\"fs-id1167829810538\">line \\(2x-y=6,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(3,0\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833382488\"><p id=\"fs-id1167833382490\">\\(y=2x-6\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829749845\"><div data-type=\"problem\" id=\"fs-id1167829749847\"><p id=\"fs-id1167836596678\">line \\(2x+3y=6,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(0,5\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833019832\"><div data-type=\"problem\" id=\"fs-id1167833019834\"><p id=\"fs-id1167836717185\">line \\(x=-4,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(-3,-5\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833058199\"><p id=\"fs-id1167829624480\">\\(x=-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836486058\"><div data-type=\"problem\" id=\"fs-id1167836486060\"><p id=\"fs-id1167836531943\">line \\(x-2=0,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(1,-2\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836391229\"><div data-type=\"problem\" id=\"fs-id1167836391231\"><p id=\"fs-id1167829619310\">line \\(y=5,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(2,-2\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836609836\"><p id=\"fs-id1167836609838\">\\(y=-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829811153\"><div data-type=\"problem\" id=\"fs-id1167824590420\"><p id=\"fs-id1167824590422\">line \\(y+2=0,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(3,-3\\right)\\)<\/div><\/div><p id=\"fs-id1167829621585\"><strong data-effect=\"bold\">Find an Equation of a Line Perpendicular to a Given Line<\/strong><\/p><p id=\"fs-id1167836526732\">In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167829752070\"><div data-type=\"problem\" id=\"fs-id1167833361655\"><p id=\"fs-id1167833361658\">line \\(y=-2x+3,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(2,2\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833047531\"><p id=\"fs-id1167836417222\">\\(y=\\frac{1}{2}x+1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836608786\"><div data-type=\"problem\" id=\"fs-id1167836608788\"><p id=\"fs-id1167829923321\">line \\(y=\\text{\u2212}x+5,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(3,3\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836701461\"><div data-type=\"problem\" id=\"fs-id1167836732331\"><p id=\"fs-id1167836732333\">line \\(y=\\frac{3}{4}x-2,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(-3,4\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836312930\"><p id=\"fs-id1167829744039\">\\(y=-\\frac{4}{3}x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836613635\"><div data-type=\"problem\" id=\"fs-id1167829596047\"><p id=\"fs-id1167829596049\">line \\(y=\\frac{2}{3}x-4,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(2,-4\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836612285\"><div data-type=\"problem\" id=\"fs-id1167829787371\"><p id=\"fs-id1167829787373\">line \\(2x-3y=8,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(4,-1\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167829693456\"><p id=\"fs-id1167836731791\">\\(y=-\\frac{3}{2}x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832977098\"><div data-type=\"problem\" id=\"fs-id1167832977101\"><p id=\"fs-id1167833175512\">line \\(4x-3y=5,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(-3,2\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836518806\"><div data-type=\"problem\" id=\"fs-id1167836518808\"><p id=\"fs-id1167824735838\">line \\(2x+5y=6,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(0,0\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836439631\"><p id=\"fs-id1167836567424\">\\(y=\\frac{5}{2}x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829908672\"><div data-type=\"problem\" id=\"fs-id1167829908674\"><p id=\"fs-id1167829714449\">line \\(4x+5y=-3,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(0,0\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830059063\"><div data-type=\"problem\" id=\"fs-id1167830059065\"><p id=\"fs-id1167822966262\">line \\(x=3,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(3,4\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833361699\"><p id=\"fs-id1167833361701\">\\(y=4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836496973\"><div data-type=\"problem\" id=\"fs-id1167829745657\"><p id=\"fs-id1167829745659\">line \\(x=-5,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(1,-2\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836729396\"><div data-type=\"problem\" id=\"fs-id1167836729398\"><p id=\"fs-id1167826077209\">line \\(x=7,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(-3,-4\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833059151\"><p id=\"fs-id1167833082323\">\\(y=-4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836327353\"><div data-type=\"problem\" id=\"fs-id1167826205702\"><p id=\"fs-id1167826205704\">line \\(x=-1,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(-4,0\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836538674\"><div data-type=\"problem\" id=\"fs-id1167836538676\"><p id=\"fs-id1167836538678\">line \\(y-3=0,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(-2,-4\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833008898\"><p id=\"fs-id1167833008900\">\\(x=-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826130658\"><div data-type=\"problem\" id=\"fs-id1167826130660\"><p id=\"fs-id1167833369088\">line \\(y-6=0,\\)<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(-5,-3\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829807550\"><div data-type=\"problem\" id=\"fs-id1167829807552\"><p id=\"fs-id1167836611143\">line <em data-effect=\"italics\">y<\/em>-axis,<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(3,4\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836598022\"><p id=\"fs-id1167836598024\">\\(y=4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836389046\"><div data-type=\"problem\" id=\"fs-id1167836389048\"><p id=\"fs-id1167833274080\">line <em data-effect=\"italics\">y<\/em>-axis,<\/p><div data-type=\"newline\"><br><\/div>point \\(\\left(2,1\\right)\\)<\/div><\/div><p id=\"fs-id1171791101176\"><strong data-effect=\"bold\">Mixed Practice<\/strong><\/p><p id=\"fs-id1167832977157\">In the following exercises, find the equation of each line. Write the equation in slope-intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167829879476\"><div data-type=\"problem\" id=\"fs-id1167829879478\"><p id=\"fs-id1167829879480\">Containing the points \\(\\left(4,3\\right)\\) and \\(\\left(8,1\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836728415\"><p id=\"fs-id1167836728417\">\\(y=-\\frac{1}{2}x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830123660\"><div data-type=\"problem\" id=\"fs-id1167830123662\"><p id=\"fs-id1167836728914\">Containing the points \\(\\left(-2,0\\right)\\) and \\(\\left(-3,-2\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829624584\"><div data-type=\"problem\" id=\"fs-id1167833061186\"><p id=\"fs-id1167833061188\">\\(m=\\frac{1}{6},\\) containing point \\(\\left(6,1\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833061247\"><p id=\"fs-id1167833061249\">\\(y=\\frac{1}{6}x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833049256\"><div data-type=\"problem\" id=\"fs-id1167836507510\"><p id=\"fs-id1167836507512\">\\(m=\\frac{5}{6},\\) containing point \\(\\left(6,7\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836533232\"><div data-type=\"problem\" id=\"fs-id1167836533234\"><p id=\"fs-id1167833338169\">Parallel to the line \\(4x+3y=6,\\) containing point \\(\\left(0,-3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833047237\"><p id=\"fs-id1167833047239\">\\(y=-\\frac{4}{3}x-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836664674\"><div data-type=\"problem\" id=\"fs-id1167836664676\"><p id=\"fs-id1167836476792\">Parallel to the line \\(2x+3y=6,\\) containing point \\(\\left(0,5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836714016\"><div data-type=\"problem\" id=\"fs-id1167836714018\"><p id=\"fs-id1167829849933\">\\(m=-\\frac{3}{4},\\) containing point \\(\\left(8,-5\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829696829\"><p>\\(y=-\\frac{3}{4}x+1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829720221\"><div data-type=\"problem\" id=\"fs-id1167829579270\"><p id=\"fs-id1167829579272\">\\(m=-\\frac{3}{5},\\) containing point \\(\\left(10,-5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833128553\"><div data-type=\"problem\" id=\"fs-id1167833128555\"><p id=\"fs-id1167833128557\">Perpendicular to the line \\(y-1=0,\\) point \\(\\left(-2,6\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836596745\"><p id=\"fs-id1167836596747\">\\(x=-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833339135\"><div data-type=\"problem\" id=\"fs-id1167833339137\"><p id=\"fs-id1167829590713\">Perpendicular to the line <em data-effect=\"italics\">y<\/em>-axis, point \\(\\left(-6,2\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836756601\"><div data-type=\"problem\" id=\"fs-id1167836756604\"><p id=\"fs-id1167836756606\">Parallel to the line \\(x=-3,\\) containing point \\(\\left(-2,-1\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829787446\"><p id=\"fs-id1167836572789\">\\(x=-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167825986925\"><div data-type=\"problem\" id=\"fs-id1167825986927\"><p id=\"fs-id1167825986929\">Parallel to the line \\(x=-4,\\) containing point \\(\\left(-3,-5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829931362\"><div data-type=\"problem\" id=\"fs-id1167832951124\"><p id=\"fs-id1167832951126\">Containing the points \\(\\left(-3,-4\\right)\\) and \\(\\left(2,-5\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833366682\"><p id=\"fs-id1167833366684\">\\(y=-\\frac{1}{5}x-\\frac{23}{5}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836309284\"><div data-type=\"problem\" id=\"fs-id1167829787935\"><p id=\"fs-id1167829787938\">Containing the points \\(\\left(-5,-3\\right)\\) and \\(\\left(4,-6\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833407736\"><div data-type=\"problem\" id=\"fs-id1167836673451\"><p id=\"fs-id1167836673453\">Perpendicular to the line \\(x-2y=5,\\) point \\(\\left(-2,2\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833345909\"><p id=\"fs-id1167833345912\">\\(y=-2x-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836623550\"><div data-type=\"problem\" id=\"fs-id1167836518250\"><p id=\"fs-id1167836518252\">Perpendicular to the line \\(4x+3y=1,\\) point \\(\\left(0,0\\right)\\)<\/p><\/div><\/div><\/div><div class=\"writing\" data-depth=\"2\" id=\"fs-id1167836690259\"><h4 data-type=\"title\">Writing Exercises<\/h4><div data-type=\"exercise\" id=\"fs-id1167824976247\"><div data-type=\"problem\" id=\"fs-id1167836600645\"><p id=\"fs-id1167836600647\">Why are all horizontal lines parallel?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836363428\"><p id=\"fs-id1167836363430\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836484625\"><div data-type=\"problem\" id=\"fs-id1167836484628\"><p id=\"fs-id1167836362164\">Explain in your own words why the slopes of two perpendicular lines must have opposite signs.<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167824732320\"><h4 data-type=\"title\">Self Check<\/h4><p id=\"fs-id1167824732325\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p><span data-type=\"media\" id=\"fs-id1167824648924\" data-alt=\"The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is \u201cconfidently\u201d, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cfind the equation of the line given the slope and y-intercept\u201d, \u201cfind an equation of the line given the slope and a point\u201d, \u201cfind an equation of the line given two points\u201d, \u201cfind an equation of a line parallel to a given line\u201d, and \u201cfind an equation of a line perpendicular to a given line\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_209_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is \u201cconfidently\u201d, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cfind the equation of the line given the slope and y-intercept\u201d, \u201cfind an equation of the line given the slope and a point\u201d, \u201cfind an equation of the line given two points\u201d, \u201cfind an equation of a line parallel to a given line\u201d, and \u201cfind an equation of a line perpendicular to a given line\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.\"><\/span><p id=\"fs-id1167829748644\"><span class=\"token\">\u24d1<\/span> What does this checklist tell you about your mastery of this section? What steps will you take to improve?<\/p><\/div><\/div><div data-type=\"glossary\" class=\"textbox shaded\"><h3 data-type=\"glossary-title\">Glossary<\/h3><dl id=\"fs-id1167836545346\"><dt>point-slope form<\/dt><dd id=\"fs-id1167836545350\">The point-slope form of an equation of a line with slope <em data-effect=\"italics\">m<\/em> and containing the point \\(\\left({x}_{1},{y}_{1}\\right)\\) is \\(y-{y}_{1}=m\\left(x-{x}_{1}\\right).\\)<\/dd><\/dl><\/div>\n","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to: <\/p>\n<ul>\n<li>Find an equation of the line given the slope and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a37c1b15afc43c8c74d2c1809695f8cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#105;&#110;&#116;&#101;&#114;&#99;&#101;&#112;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Find an equation of the line given the slope and a point<\/li>\n<li>Find an equation of the line given two points<\/li>\n<li>Find an equation of a line parallel to a given line<\/li>\n<li>Find an equation of a line perpendicular to a given line<\/li>\n<\/ul>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836287977\" class=\"be-prepared\">\n<p id=\"fs-id1167836532223\">Before you get started, take this readiness quiz.<\/p>\n<ol id=\"fs-id1167836546304\" type=\"1\">\n<li>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dab6ccb4e36ead82e5c09223a3c48c49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"82\" style=\"vertical-align: -6px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/987da0d0-2366-47d6-aa25-904e24991866#fs-id1167829789060\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3c5a8f50ac7c9a7b391a8ab3c10e9a91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"114\" style=\"vertical-align: -4px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/987da0d0-2366-47d6-aa25-904e24991866#fs-id1167829741770\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Solve for <em data-effect=\"italics\">y<\/em>: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0e0b1d4dcd659fc157d0904821bce0b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#51;&#61;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"151\" style=\"vertical-align: -4px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/b03538a1-8a7b-4158-a68b-e0e8a24c9fd4#fs-id1167835229496\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<\/ol>\n<\/div>\n<p>How do online companies know that \u201cyou may also like\u201d a particular item based on something you just ordered? How can economists know how a rise in the minimum wage will affect the unemployment rate? How do medical researchers create drugs to target cancer cells? How can traffic engineers predict the effect on your commuting time of an increase or decrease in gas prices? It\u2019s all mathematics.<\/p>\n<p id=\"fs-id1167836300272\">The physical sciences, social sciences, and the business world are full of situations that can be modeled with linear equations relating two variables. To create a mathematical model of a linear relation between two variables, we must be able to find the equation of the line. In this section, we will look at several ways to write the equation of a line. The specific method we use will be determined by what information we are given.<\/p>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836601891\">\n<h3 data-type=\"title\">Find an Equation of the Line Given the Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/h3>\n<p id=\"fs-id1167829650554\">We can easily determine the slope and intercept of a line if the equation is written in slope-intercept form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08f367b1234ecf1fe2aac0e288fe4feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"92\" style=\"vertical-align: -4px;\" \/> Now we will do the reverse\u2014we will start with the slope and <em data-effect=\"italics\">y<\/em>-intercept and use them to find the equation of the line.<\/p>\n<div data-type=\"example\" id=\"fs-id1167833054952\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836640431\">\n<div data-type=\"problem\" id=\"fs-id1167833021115\">\n<p id=\"fs-id1167836706728\">Find the equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d5b6e32514b23269b5f16f192142a89e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829717392\">\n<p id=\"fs-id1167829645042\">Since we are given the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line, we can substitute the needed values into the slope-intercept form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08f367b1234ecf1fe2aac0e288fe4feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<table id=\"fs-id1167836686077\" class=\"unnumbered unstyled\" summary=\"Name the slope. m equals negative 9. Name the y-intercept. The y-intercept is (0, negative 4). Substitute the values into y equals m x plus b. y equals negative 9 x plus negative 4. The m and negative 4 are both emphasized in red. The b and negative 4 are both emphasized in blue. This simplifies to y equals negative 9 x minus 4.\" data-label=\"\">\n<tbody>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Name the slope.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836341614\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Name the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Substitute the values into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08f367b1234ecf1fe2aac0e288fe4feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836615581\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829599074\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833050669\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_001e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836614830\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836730567\">\n<div data-type=\"problem\" id=\"fs-id1167833020885\">\n<p id=\"fs-id1167829905530\">Find the equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0700364398eac9320f4d6eebefa6d6b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-39c99385521a53a652ee24ad5c5d1086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836688878\">\n<p id=\"fs-id1167833365618\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ff4131ac0dd063a1b9000c0277f6ecb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829614246\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833257642\">\n<div data-type=\"problem\" id=\"fs-id1167836556216\">\n<p id=\"fs-id1167824652508\">Find the equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> and <em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2a02f2acb07c1c1b796ba6e9846dec18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836692872\">\n<p id=\"fs-id1167836546955\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4597e9a5dd1ad5e5267c465d2e5539d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836415102\">Sometimes, the slope and intercept need to be determined from the graph.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836450394\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167825091753\">\n<div data-type=\"problem\" id=\"fs-id1167836608164\">\n<p id=\"fs-id1167829597566\">Find the equation of the line shown in the graph.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167830123714\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 3, negative 6), (0, negative 4), (3, negative 2), and (6, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_002_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 3, negative 6), (0, negative 4), (3, negative 2), and (6, 0).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836526766\">\n<p id=\"fs-id1167826130705\">We need to find the slope and <em data-effect=\"italics\">y<\/em>-intercept of the line from the graph so we can substitute the needed values into the slope-intercept form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08f367b1234ecf1fe2aac0e288fe4feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1167833310695\">To find the slope, we choose two points on the graph.<\/p>\n<p id=\"fs-id1167830077375\">The <em data-effect=\"italics\">y<\/em>-intercept is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-42f3c0bd5adc0ec0fa1707d7989e5c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> and the graph passes through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-28a6016d97459bf95f87ab98a0a40558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<table id=\"fs-id1167829860698\" class=\"unnumbered unstyled\" summary=\"Find the slope, by counting the rise and run. m equals rise divided by run. m equals 2 divided by 3. Find the y-intercept. y-intercept is (0, negative 4). Substitute the values into y equals m x plus b. y equals 2 divided by 3 x minus 4. The m and 2 divided by 3 are both emphasized in red. The b and negative 4 are emphasized in blue.\" data-label=\"\">\n<tbody>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Find the slope, by counting the rise and run.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836615805\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829594439\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Find the <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836560229\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Substitute the values into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08f367b1234ecf1fe2aac0e288fe4feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167826171770\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836513064\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_003e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836536600\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836318591\">\n<div data-type=\"problem\" id=\"fs-id1167836321281\">\n<p id=\"fs-id1167836628664\">Find the equation of the line shown in the graph.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167824700008\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 5, negative 2), (0, 1), and (5, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_004_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 5, negative 2), (0, 1), and (5, 4).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829690492\">\n<p id=\"fs-id1167836333597\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b2ff9b46a2d4804a1ae62bd9c7e1c43f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833056308\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836624567\">\n<div data-type=\"problem\" id=\"fs-id1167826025447\">\n<p id=\"fs-id1167829595577\">Find the equation of the line shown in the graph.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836607892\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 5), (3, negative 1), and (6, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_005_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 5), (3, negative 1), and (6, 3).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167824735214\">\n<p id=\"fs-id1167832956878\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-72b1ab9f028b3f33ac825a1027435960_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167829791300\">\n<h3 data-type=\"title\">Find an Equation of the Line Given the Slope and a Point<\/h3>\n<p id=\"fs-id1167825913830\">Finding an equation of a line using the slope-intercept form of the equation works well when you are given the slope and <em data-effect=\"italics\">y<\/em>-intercept or when you read them off a graph. But what happens when you have another point instead of the <em data-effect=\"italics\">y<\/em>-intercept?<\/p>\n<p id=\"fs-id1167836433751\">We are going to use the slope formula to derive another form of an equation of the line.<\/p>\n<p id=\"fs-id1167836619863\">Suppose we have a line that has slope <em data-effect=\"italics\">m<\/em> and that contains some specific point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-daf7d3000a611d6a6b02b6093c3dfb1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#44;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -4px;\" \/> and some other point, which we will just call <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0ab61ec2033ed5b69d0447eac5d6a4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/> We can write the slope of this line and then change it to a different form.<\/p>\n<p id=\"fs-id1167829755664\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c4d9365a572d38d4e38b561d98daff65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#125;&#123;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#32;&#98;&#111;&#116;&#104;&#32;&#115;&#105;&#100;&#101;&#115;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#32;&#98;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#125;&#123;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#101;&#119;&#114;&#105;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#32;&#119;&#105;&#116;&#104;&#32;&#116;&#104;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#101;&#114;&#109;&#115;&#32;&#111;&#110;&#32;&#116;&#104;&#101;&#32;&#108;&#101;&#102;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"685\" style=\"vertical-align: -43px;\" \/><\/p>\n<p id=\"fs-id1167833008035\">This format is called the <span data-type=\"term\">point-slope form<\/span> of an equation of a line.<\/p>\n<div data-type=\"note\" id=\"fs-id1167824764782\">\n<div data-type=\"title\">Point-slope Form of an Equation of a Line<\/div>\n<p id=\"fs-id1167829811866\">The <strong data-effect=\"bold\">point-slope form<\/strong> of an equation of a line with slope <em data-effect=\"italics\">m<\/em> and containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-daf7d3000a611d6a6b02b6093c3dfb1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#44;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -4px;\" \/> is:<\/p>\n<div data-type=\"equation\" id=\"fs-id1171792805591\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1167829936919\">We can use the point-slope form of an equation to find an equation of a line when we know the slope and at least one point. Then, we will rewrite the equation in slope-intercept form. Most applications of linear equations use the the slope-intercept form.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836554239\" class=\"textbox textbox--examples\">\n<div data-type=\"title\">How to Find an Equation of a Line Given a Point and the Slope<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833379832\">\n<div data-type=\"problem\" id=\"fs-id1167826204850\">\n<p id=\"fs-id1167836600443\">Find an equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6fae7ea410efdec23083d9f11b3cee98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e4afd5dbc275cebe3faa56503d301afd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836543755\"><span data-type=\"media\" id=\"fs-id1167832940173\" data-alt=\"Step 1 is to identify the slope. The slope is given. m equals negative 1 divided by 3.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_007a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to identify the slope. The slope is given. m equals negative 1 divided by 3.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167826077317\" data-alt=\"Step 2 is to identify the point. The point is given. x 1 is 6 and y 1 is negative 4.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_007b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to identify the point. The point is given. x 1 is 6 and y 1 is negative 4.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167832926786\" data-alt=\"Step 3 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 4 equals negative 1 divided by 3 times the quantity x minus 6 in parentheses. This simplifies to y plus 4 equals negative 1 divided by 3 times x plus 2.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_007c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 4 equals negative 1 divided by 3 times the quantity x minus 6 in parentheses. This simplifies to y plus 4 equals negative 1 divided by 3 times x plus 2.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167836357296\" data-alt=\"Step 4 is to write the equation in slope-intercept form. y equals negative 1 divided by 3 times x minus 2.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_007d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to write the equation in slope-intercept form. y equals negative 1 divided by 3 times x minus 2.\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167826102710\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836789252\">\n<div data-type=\"problem\" id=\"fs-id1167826204767\">\n<p id=\"fs-id1167836728250\">Find the equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e21a900bf7a274ff797f019d918bacc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/> and containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1fe45adde4722ec76f7dc6a6e853dce8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829807832\">\n<p id=\"fs-id1167829860129\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-19fe345b0bd5f56c12ee603334699658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167832939589\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167832956627\">\n<div data-type=\"problem\" id=\"fs-id1167836800483\">\n<p id=\"fs-id1167836294992\">Find the equation of a line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-31f9f5e0c30ce6e4e9018dba6ba129f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> and containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ce54b55c01828f1105b9c88ad5618787_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829627970\">\n<p id=\"fs-id1167833052972\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-35a5aae349c3d632c09f51514b856f70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167824704952\">We list the steps for easy reference.<\/p>\n<div data-type=\"note\" id=\"fs-id1167826205373\" class=\"howto\">\n<div data-type=\"title\">To find an equation of a line given the slope and a point.<\/div>\n<ol id=\"fs-id1167825011557\" type=\"1\" class=\"stepwise\">\n<li>Identify the slope.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167836502652\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836607675\">\n<div data-type=\"problem\" id=\"fs-id1167833186433\">\n<p id=\"fs-id1167824976173\">Find an equation of a horizontal line that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b6635d1a0e047e3f5e38f55c51952e9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829784999\">\n<p id=\"fs-id1167833081974\">Every horizontal line has slope 0. We can substitute the slope and points into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/p>\n<table id=\"fs-id1167833326479\" class=\"unnumbered unstyled\" summary=\"Identify the slope. m equals 0. Identify the point. x 1 is negative 2 and y 1 is negative 6. Substitute the values into y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 6 equals 0 times the quantity x minus negative 2 in parentheses. This simplifies to y plus 6 equals 0 or y equals negative 6. Write in slope-intercept form. It is in y-form, but could be written y equals 0 x minus 6. Did we end up with the form of a horizontal line y equals a?\" data-label=\"\">\n<tbody>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Identify the slope.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836689589\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Identify the point.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167824734208\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Substitute the values into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836775057\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833329257\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833328934\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167822996903\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_008f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Write in slope-intercept form.<\/td>\n<td data-valign=\"top\" data-align=\"left\">It is in <em data-effect=\"italics\">y<\/em>-form, but could be written <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c05918d454ab7ab430f7081b5089941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#120;&#45;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167833025091\">Did we end up with the form of a horizontal line, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-73a604cdd7251fd21e38d271cc2ee477_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#97;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"50\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167824811964\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836509248\">\n<div data-type=\"problem\" id=\"fs-id1167833009418\">\n<p id=\"fs-id1167836356562\">Find the equation of a horizontal line containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-93cf337bc9088e2395dab132c331defc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833377584\">\n<p id=\"fs-id1167829752219\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-48a5d37560b8f593c417bc913eae1b98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836409181\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833158283\">\n<div data-type=\"problem\" id=\"fs-id1167836312136\">\n<p id=\"fs-id1167829719636\">Find the equation of a horizontal line containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-555a666c2edb336aba059b8db5a9810e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829595237\">\n<p id=\"fs-id1167836625469\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0621c4f761e7864714642fcc62d4c42f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836335402\">\n<h3 data-type=\"title\">Find an Equation of the Line Given Two Points<\/h3>\n<p id=\"fs-id1167836398532\">When real-world data is collected, a linear model can be created from two data points. In the next example we\u2019ll see how to find an equation of a line when just two points are given.<\/p>\n<p id=\"fs-id1167836595901\">So far, we have two options for finding an equation of a line: slope-intercept or point-slope. When we start with two points, it makes more sense to use the point-slope form.<\/p>\n<p id=\"fs-id1167826130820\">But then we need the slope. Can we find the slope with just two points? Yes. Then, once we have the slope, we can use it and one of the given points to find the equation.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829715551\" class=\"textbox textbox--examples\">\n<div data-type=\"title\">How to Find the Equation of a Line Given Two Points<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829893884\">\n<div data-type=\"problem\" id=\"fs-id1167823013300\">\n<p id=\"fs-id1167836329684\">Find an equation of a line that contains the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d29d505cec09336aa569e1cca8670699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8fbb5d034d8bc7481119846ba5facddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836611614\"><span data-type=\"media\" id=\"fs-id1167829853073\" data-alt=\"Step 1 is to find the slope using the given points. Find the slope of the line through (negative 3, negative 1) and (2, and negative 2). m equals the quotient of y 2 minus y 1 in parentheses and x 2 minus x 1 in parentheses. m equals the quotient of negative 2 minus negative 1 in parentheses and 2 minus negative 3 in parentheses. m equals negative 1 divided by 5.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_009a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to find the slope using the given points. Find the slope of the line through (negative 3, negative 1) and (2, and negative 2). m equals the quotient of y 2 minus y 1 in parentheses and x 2 minus x 1 in parentheses. m equals the quotient of negative 2 minus negative 1 in parentheses and 2 minus negative 3 in parentheses. m equals negative 1 divided by 5.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167829720040\" data-alt=\"Step 2 is to identify the point. Choose either point. x 1 is 2 and y 1 is negative 2.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_009b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to identify the point. Choose either point. x 1 is 2 and y 1 is negative 2.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167825836127\" data-alt=\"Step 3 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 2 equals negative 1 divided by 5 times the quantity x minus 2 in parentheses. This simplifies to y plus 2 equals negative 1 divided by 5 times x plus 2 divided by 5.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_009c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus negative 2 equals negative 1 divided by 5 times the quantity x minus 2 in parentheses. This simplifies to y plus 2 equals negative 1 divided by 5 times x plus 2 divided by 5.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167829619192\" data-alt=\"Step 4 is to write the equation in slope-intercept form. y equals negative 1 divided by 5 times x minus 8 divided by 5.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_009d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to write the equation in slope-intercept form. y equals negative 1 divided by 5 times x minus 8 divided by 5.\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836534523\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836433959\">\n<div data-type=\"problem\" id=\"fs-id1167824653042\">\n<p id=\"fs-id1167823012200\">Find the equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ecc91b8d5e91ea23c08fcf2ee52342c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7e365d1928b8305e44397b97f2500425_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829692284\">\n<p id=\"fs-id1167836415614\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f4db4c61c795e9cd70c1f7fda8713a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"91\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836730055\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829893622\">\n<div data-type=\"problem\" id=\"fs-id1167836640506\">\n<p id=\"fs-id1167836683962\">Find the equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ebe785a1a1f173c2cb47dc17a15cdc63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-65261358a1796b5039acb865fda2665a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836575727\">\n<p id=\"fs-id1167833096636\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-162c857d9971f863560f01b41248cea4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836433564\">The steps are summarized here.<\/p>\n<div data-type=\"note\" id=\"fs-id1167836293926\" class=\"howto\">\n<div data-type=\"title\">To find an equation of a line given two points.<\/div>\n<ol id=\"fs-id1167832980824\" type=\"1\" class=\"stepwise\">\n<li>Find the slope using the given points. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e8828e33f8f597c9b3df95aa3a0786c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#95;&#123;&#50;&#125;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#125;&#123;&#123;&#120;&#125;&#95;&#123;&#50;&#125;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"81\" style=\"vertical-align: -9px;\" \/><\/li>\n<li>Choose one point.<\/li>\n<li>Substitute the values into the point-slope form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167836596902\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833009830\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836544330\">Find an equation of a line that contains the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5aa29da239e6fed61429835a4b4444af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9edb132d6e0d9a8e7cebf538ef2f84a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167836800401\">Again, the first step will be to find the slope.<\/p>\n<p id=\"fs-id1167836283420\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5198d07fadbb997cc5e459259db1b002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#105;&#110;&#100;&#32;&#116;&#104;&#101;&#32;&#115;&#108;&#111;&#112;&#101;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#108;&#105;&#110;&#101;&#32;&#116;&#104;&#114;&#111;&#117;&#103;&#104;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#95;&#123;&#50;&#125;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#125;&#123;&#123;&#120;&#125;&#95;&#123;&#50;&#125;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#45;&#53;&#125;&#123;&#45;&#51;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#109;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#49;&#125;&#123;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#115;&#108;&#111;&#112;&#101;&#32;&#105;&#115;&#32;&#117;&#110;&#100;&#101;&#102;&#105;&#110;&#101;&#100;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"215\" width=\"661\" style=\"vertical-align: -102px;\" \/><\/p>\n<p id=\"fs-id1167833397134\">This tells us it is a vertical line. Both of our points have an <em data-effect=\"italics\">x<\/em>-coordinate of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d36c434a1919e0aaa1a4125fdaa40853_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/> So our equation of the line is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-86f872935a384592f05d5fdc077a0a0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/> Since there is no <em data-effect=\"italics\">y<\/em>, we cannot write it in slope-intercept form.<\/p>\n<p id=\"fs-id1167833381342\">You may want to sketch a graph using the two given points. Does your graph agree with our conclusion that this is a vertical line?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836544022\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836520875\">\n<p id=\"fs-id1167836485974\">Find the equation of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b932df7404bba7c4812c40fc6d0d4b4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec1f58e3551111ede13ce2158eff570f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836701061\">\n<p id=\"fs-id1167829752657\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836532553\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836619179\">\n<div data-type=\"problem\" id=\"fs-id1167833407674\">\n<p id=\"fs-id1167836646048\">Find the equaion of a line containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6bd03bb09a34e49dd9f3ebf548e3dab1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cc8ce4d4bfac2c0316c1f8dcfcd2d3f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833023052\">\n<p id=\"fs-id1167836289656\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b3dc975a98ccada6f136856736d7df06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836614877\">We have seen that we can use either the slope-intercept form or the point-slope form to find an equation of a line. Which form we use will depend on the information we are given.<\/p>\n<table id=\"fs-id1167836293795\" class=\"unnumbered\" summary=\"The table is titled To Write and Equation of a Line. It has three columns labeled \u201cIf given,\u201d \u201cUse,\u201d, and \u201cForm.\u201d The first row shows that if the slope and y intercept are given, use the slope-intercept form, which is y equals mx plus b. The second row shows that if the slope and a point are given, use the point-slope form, which is y minus y sub 1 equals m times the quantity x minus x sub 1.\">\n<thead>\n<tr>\n<th colspan=\"3\" data-valign=\"middle\" data-align=\"center\">To Write an Equation of a Line<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">If given:<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">Use:<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">Form:<\/strong><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Slope and <em data-effect=\"italics\">y<\/em>-intercept<\/td>\n<td data-valign=\"middle\" data-align=\"left\">slope-intercept<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Slope and a point<\/td>\n<td data-valign=\"middle\" data-align=\"left\">point-slope<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Two points<\/td>\n<td data-valign=\"middle\" data-align=\"left\">point-slope<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\">Find an Equation of a Line Parallel to a Given Line<\/h3>\n<p id=\"fs-id1167833047491\">Suppose we need to find an equation of a line that passes through a specific point and is parallel to a given line. We can use the fact that parallel lines have the same slope. So we will have a point and the slope\u2014just what we need to use the point-slope equation.<\/p>\n<p id=\"fs-id1167836312500\">First, let\u2019s look at this graphically.<\/p>\n<p id=\"fs-id1167829716102\">This graph shows <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc617a1e7c2cc45ad6eac438f484cab7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/> We want to graph a line parallel to this line and passing through the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8214cd1dae89c5047c3dc6e12087cf14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836320481\" data-alt=\"This figure has a graph of a straight line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The point (negative 2, 1) is plotted. The line does not go through the point (negative 2, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_010_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The point (negative 2, 1) is plotted. The line does not go through the point (negative 2, 1).\" \/><\/span><\/p>\n<p id=\"fs-id1167836697298\">We know that parallel lines have the same slope. So the second line will have the same slope as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc617a1e7c2cc45ad6eac438f484cab7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/> That slope is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bbe9c176bd316557a924d0367bc5c053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#97;&#114;&#97;&#108;&#108;&#101;&#108;&#32;&#125;&#61;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"60\" style=\"vertical-align: -8px;\" \/> We\u2019ll use the notation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-317be5f65ae274c1a6831a4dd467bc71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#97;&#114;&#97;&#108;&#108;&#101;&#108;&#32;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"22\" style=\"vertical-align: -8px;\" \/> to represent the slope of a line parallel to a line with slope <em data-effect=\"italics\">m<\/em>. (Notice that the subscript || looks like two parallel lines.)<\/p>\n<p id=\"fs-id1167829743890\">The second line will pass through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a17b6fae5de6824bd84fe506e4e9ac7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id1167836289727\">To graph the line, we start at<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and count out the rise and run.<\/p>\n<p id=\"fs-id1167836700923\">With <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1ee3bb14bbe97a1114d697f8b45a9f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> (or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8f178cea1ff3381ad9c61f772e830d21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"48\" style=\"vertical-align: -7px;\" \/>), we count out the rise 2 and the run 1. We draw the line, as shown in the graph.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167829713321\" data-alt=\"This figure has a graph of a two straight lines on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The first line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The points (negative 2, 1) and (negative 1, 3) are plotted. The second line goes through the points (negative 2, 1) and (negative 1, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_011_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a two straight lines on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The first line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The points (negative 2, 1) and (negative 1, 3) are plotted. The second line goes through the points (negative 2, 1) and (negative 1, 3).\" \/><\/span><\/p>\n<p id=\"fs-id1167829696351\">Do the lines appear parallel? Does the second line pass through<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-64cc9ac2843b8321cd820f56f36aa67f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1167836305436\">We were asked to graph the line, now let\u2019s see how to do this algebraically.<\/p>\n<p id=\"fs-id1167836493048\">We can use either the slope-intercept form or the point-slope form to find an equation of a line. Here we know one point and can find the slope. So we will use the point-slope form.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836300038\" class=\"textbox textbox--examples\">\n<div data-type=\"title\">How to Find the Equation of a Line Parallel to a Given Line and a Point<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836410330\">\n<p id=\"fs-id1167836596689\">Find an equation of a line parallel to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8214cd1dae89c5047c3dc6e12087cf14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836623976\"><span data-type=\"media\" id=\"fs-id1167836686744\" data-alt=\"Step 1 is to find the slope of the given line. The line is in slope-intercept form, y equals 2 x minus 3. m equals 2.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to find the slope of the given line. The line is in slope-intercept form, y equals 2 x minus 3. m equals 2.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167836508752\" data-alt=\"Step 2 is to find the slope of the parallel line. Parallel lines have the same slope. m equals 2.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to find the slope of the parallel line. Parallel lines have the same slope. m equals 2.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167836313488\" data-alt=\"Step 3 is to identify the point. The given point is (negative 2, 1). x 1 is negative 2 and y 1 is 1.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to identify the point. The given point is (negative 2, 1). x 1 is negative 2 and y 1 is 1.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167829596586\" data-alt=\"Step 4 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus 1 equals 2 times the quantity x minus negative 2 in parentheses. This simplifies to y minus 1 equals 2 x plus 4.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus 1 equals 2 times the quantity x minus negative 2 in parentheses. This simplifies to y minus 1 equals 2 x plus 4.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167836635332\" data-alt=\"Step 5 is to write the equation in slope-intercept form. y equals 2 x plus 5.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012e_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 5 is to write the equation in slope-intercept form. y equals 2 x plus 5.\" \/><\/span><\/p>\n<p id=\"fs-id1167833061296\">Look at graph with the parallel lines shown previously. Does this equation make sense? What is the <em data-effect=\"italics\">y<\/em>-intercept of the line? What is the slope?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836580165\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836611133\">\n<div data-type=\"problem\" id=\"fs-id1167829894247\">\n<p id=\"fs-id1167829683684\">Find an equation of a line parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15253001234eb31db5eff50664eacd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ab3a70b72359d6cbd0b2e85e99c27924_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167825660367\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-664b8b828b69575feb482f8daae0f302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167832999699\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836628180\">\n<div data-type=\"problem\" id=\"fs-id1167833224723\">\n<p id=\"fs-id1167824732116\">Find an equation of a line parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6b9d262703706430bfe9be960d499e29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c61ef193c0853840ed1f0892294eb352_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/p>\n<p>Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836289214\">\n<p id=\"fs-id1167836538340\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-755037b7c634e8f6760f24bebd6f5a2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"howto\">\n<div data-type=\"title\">Find an equation of a line parallel to a given line.<\/div>\n<ol id=\"fs-id1167829879306\" type=\"1\" class=\"stepwise\">\n<li>Find the slope of the given line.<\/li>\n<li>Find the slope of the parallel line.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836513856\">\n<h3 data-type=\"title\">Find an Equation of a Line Perpendicular to a Given Line<\/h3>\n<p id=\"fs-id1167826204724\">Now, let\u2019s consider perpendicular lines. Suppose we need to find a line passing through a specific point and which is perpendicular to a given line. We can use the fact that perpendicular lines have slopes that are negative reciprocals. We will again use the point-slope equation, like we did with parallel lines.<\/p>\n<p id=\"fs-id1167829834014\">This graph shows <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc617a1e7c2cc45ad6eac438f484cab7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/> Now, we want to graph a line perpendicular to this line and passing through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8214cd1dae89c5047c3dc6e12087cf14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span data-type=\"media\" id=\"fs-id1167829578789\" data-alt=\"This figure has a graph of a straight line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The point (negative 2, 1) is plotted. The line does not go through the point (negative 2, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_012_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The point (negative 2, 1) is plotted. The line does not go through the point (negative 2, 1).\" \/><\/span><\/p>\n<p id=\"fs-id1167836534688\">We know that perpendicular lines have slopes that are negative reciprocals.<\/p>\n<p id=\"fs-id1167836553112\">We\u2019ll use the notation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-31912bd9236ad3cffb6c6d558e090310_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#32;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\" \/> to represent the slope of a line perpendicular to a line with slope <em data-effect=\"italics\">m<\/em>. (Notice that the subscript <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-818d7e2604a46241a4cf6c84b3585588_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#101;&#114;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/> looks like the right angles made by two perpendicular lines.)<\/p>\n<div data-type=\"equation\" id=\"fs-id1167833022890\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0961909b9c000707210cfea5f05f0893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#121;&#61;&#50;&#120;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#112;&#101;&#110;&#100;&#105;&#99;&#117;&#108;&#97;&#114;&#32;&#108;&#105;&#110;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#109;&#61;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#32;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"272\" style=\"vertical-align: -17px;\" \/><\/div>\n<p id=\"fs-id1167836575849\">We now know the perpendicular line will pass through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4b7eaad8f9e07ff9f98b1b5ff61a1de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#32;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"79\" style=\"vertical-align: -6px;\" \/><\/p>\n<p id=\"fs-id1167829627541\">To graph the line, we will start at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and count out the rise <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> and the run 2. Then we draw the line.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167830095268\" data-alt=\"This figure has a graph of two perpendicular straight lines on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The first line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The points (negative 2, 1) and (0, 0) are plotted. A right triangle is drawn connecting the points (negative 2, 1), (negative 2, 0), and (0, 0). The second line goes through the points (negative 2, 1) and (0, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_013_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of two perpendicular straight lines on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The first line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The points (negative 2, 1) and (0, 0) are plotted. A right triangle is drawn connecting the points (negative 2, 1), (negative 2, 0), and (0, 0). The second line goes through the points (negative 2, 1) and (0, 0).\" \/><\/span><\/p>\n<p id=\"fs-id1167836296407\">Do the lines appear perpendicular? Does the second line pass through<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-64cc9ac2843b8321cd820f56f36aa67f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1167829627933\">We were asked to graph the line, now, let\u2019s see how to do this algebraically.<\/p>\n<p id=\"fs-id1167825703151\">We can use either the slope-intercept form or the point-slope form to find an equation of a line. In this example we know one point, and can find the slope, so we will use the point-slope form.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829737780\" class=\"textbox textbox--examples\">\n<div data-type=\"title\">How to Find the Equation of a Line Perpendicular to a Given Line and a Point<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833338703\">\n<div data-type=\"problem\" id=\"fs-id1167836570858\">\n<p id=\"fs-id1167836790223\">Find an equation of a line perpendicular to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8214cd1dae89c5047c3dc6e12087cf14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836539459\"><span data-type=\"media\" id=\"fs-id1167836527833\" data-alt=\"Step 1 is to find the slope of the given line. The line is in slope-intercept form, y equals 2 x minus 3. m equals 2.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to find the slope of the given line. The line is in slope-intercept form, y equals 2 x minus 3. m equals 2.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167836286660\" data-alt=\"Step 2 is to find the slope of the perpendicular line. The slopes of perpendicular lines are negative reciprocals. m equals negative 1 divided by 2\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to find the slope of the perpendicular line. The slopes of perpendicular lines are negative reciprocals. m equals negative 1 divided by 2\" \/><\/span><span data-type=\"media\" id=\"fs-id1167836731058\" data-alt=\"Step 3 is to identify the point. The given point is (negative 2, 1). x 1 is negative 2 and y 1 is 1.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to identify the point. The given point is (negative 2, 1). x 1 is negative 2 and y 1 is 1.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167832940562\" data-alt=\"Step 4 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus 1 equals negative 1 divided by 2 times the quantity x minus negative 2 in parentheses. This simplifies to y minus 1 equals negative 1 divided by 2 times the quantity x plus 2 in parentheses. This further simplifies to y minus 1 equals negative 1 divided by 2 times x minus 1.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to substitute the values into the point-slope form y minus y 1 equals m times the quantity x minus x 1 in parentheses. y minus 1 equals negative 1 divided by 2 times the quantity x minus negative 2 in parentheses. This simplifies to y minus 1 equals negative 1 divided by 2 times the quantity x plus 2 in parentheses. This further simplifies to y minus 1 equals negative 1 divided by 2 times x minus 1.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167836321997\" data-alt=\"Step 5 is to write the equation in slope-intercept form. y equals negative 1 divided by 2 times x.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_014e_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 5 is to write the equation in slope-intercept form. y equals negative 1 divided by 2 times x.\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836510503\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833364838\">\n<div data-type=\"problem\" id=\"fs-id1167836615040\">\n<p id=\"fs-id1167836399749\">Find an equation of a line perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15253001234eb31db5eff50664eacd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ab3a70b72359d6cbd0b2e85e99c27924_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167830093016\">\n<p id=\"fs-id1167832940087\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cf9d2d99de5249f15aead3eb013f4e38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829739244\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167832930300\">\n<div data-type=\"problem\" id=\"fs-id1167836390247\">\n<p id=\"fs-id1167836790119\">Find an equation of a line perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6b9d262703706430bfe9be960d499e29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c61ef193c0853840ed1f0892294eb352_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167829590431\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a4fbd762ab5dc494da02f8e86c299946_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#43;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836513068\" class=\"howto\">\n<div data-type=\"title\">Find an equation of a line perpendicular to a given line.<\/div>\n<ol id=\"fs-id1167833369074\" type=\"1\" class=\"stepwise\">\n<li>Find the slope of the given line.<\/li>\n<li>Find the slope of the perpendicular line.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167833061157\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833382937\">\n<div data-type=\"problem\" id=\"fs-id1167836329294\">\n<p id=\"fs-id1167836630433\">Find an equation of a line perpendicular to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-28a6016d97459bf95f87ab98a0a40558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836340178\">\n<p id=\"fs-id1167836549844\">Again, since we know one point, the point-slope option seems more promising than the slope-intercept option. We need the slope to use this form, and we know the new line will be perpendicular to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-293cae06997efc99f11b7f0e51bfa8ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: 0px;\" \/> This line is vertical, so its perpendicular will be horizontal. This tells us the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7da0942a05a8670c679786afe3987982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#32;&#125;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"64\" style=\"vertical-align: -3px;\" \/><\/p>\n<p id=\"fs-id1167836520781\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1aaa519dc60fa62ac3893604db540f53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#32;&#116;&#104;&#101;&#32;&#112;&#111;&#105;&#110;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#32;&#116;&#104;&#101;&#32;&#115;&#108;&#111;&#112;&#101;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#112;&#101;&#114;&#112;&#101;&#110;&#100;&#105;&#99;&#117;&#108;&#97;&#114;&#32;&#108;&#105;&#110;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#118;&#97;&#108;&#117;&#101;&#115;&#32;&#105;&#110;&#116;&#111;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#109;&#125;&#95;&#123;&#92;&#112;&#101;&#114;&#112;&#32;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#43;&#50;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#121;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"161\" width=\"631\" style=\"vertical-align: -59px;\" \/><\/p>\n<p id=\"fs-id1167836533799\">Sketch the graph of both lines. On your graph, do the lines appear to be perpendicular?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836520482\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829750618\">\n<div data-type=\"problem\" id=\"fs-id1167833274749\">\n<p id=\"fs-id1167836429672\">Find an equation of a line that is perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ab6d75552154ad6bd9e389ff4994fd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/>. Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836486854\">\n<p id=\"fs-id1167836433816\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ee7bf59b42611ad4534a6d8ca47648e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833020343\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167829628068\">\n<p id=\"fs-id1167836701558\">Find an equation of a line that is perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9ed3f84e4d9fd37e7c85bf5177357fe0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829594832\">\n<p id=\"fs-id1167832935722\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9f371b4e77462e28d9f6119571c92982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829789981\">In <a href=\"#fs-id1167833061157\" class=\"autogenerated-content\">(Figure)<\/a>, we used the point-slope form to find the equation. We could have looked at this in a different way.<\/p>\n<p id=\"fs-id1167836539730\">We want to find a line that is perpendicular to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-28a6016d97459bf95f87ab98a0a40558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> This graph shows us the line<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> and the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-28a6016d97459bf95f87ab98a0a40558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span data-type=\"media\" data-alt=\"This figure has a graph of a straight vertical line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (5, 0), (5, 1), and (5, 2). The point (3, negative 2) is plotted. The line does not go through the point (3, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_015_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight vertical line and a point on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (5, 0), (5, 1), and (5, 2). The point (3, negative 2) is plotted. The line does not go through the point (3, negative 2).\" \/><\/span><\/p>\n<p id=\"fs-id1167826206025\">We know every line perpendicular to a vertical line is horizontal, so we will sketch the horizontal line through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-28a6016d97459bf95f87ab98a0a40558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span data-type=\"media\" data-alt=\"This figure has a graph of a straight vertical line and a straight horizontal line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The vertical line goes through the points (5, 0), (5, 1), and (5, 2). The horizontal line goes through the points (negative 2, negative 2), (0, negative 2), (3, negative 2), and (6, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_016_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight vertical line and a straight horizontal line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The vertical line goes through the points (5, 0), (5, 1), and (5, 2). The horizontal line goes through the points (negative 2, negative 2), (0, negative 2), (3, negative 2), and (6, negative 2).\" \/><\/span><\/p>\n<p id=\"fs-id1167829690001\">Do the lines appear perpendicular?<\/p>\n<p id=\"fs-id1167836418683\">If we look at a few points on this horizontal line, we notice they all have <em data-effect=\"italics\">y<\/em>-coordinates of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d36c434a1919e0aaa1a4125fdaa40853_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/> So, the equation of the line perpendicular to the vertical line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6c505f72fcfe61f7d09cd56185cc12d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"example\" id=\"fs-id1167836554451\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833257675\">\n<div data-type=\"problem\" id=\"fs-id1167829807866\">\n<p id=\"fs-id1167829743413\">Find an equation of a line that is perpendicular to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-91f9ec631e44f3d108457c2f8adad27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-788fb6cb9a282b67c60679640020d797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167824651086\">\n<p id=\"fs-id1167829812775\">The line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-91f9ec631e44f3d108457c2f8adad27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/> is a horizontal line. Any line perpendicular to it must be vertical, in the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5c2ae728b9a161e044125a0dc6c913c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#97;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"47\" style=\"vertical-align: 0px;\" \/> Since the perpendicular line is vertical and passes through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-48a45d0f6545ea28ae43545e08bd83c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> every point on it has an <em data-effect=\"italics\">x<\/em>-coordinate of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cfa36400e576c82fd4847d2da37b1d56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/> The equation of the perpendicular line is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id1167833020048\">You may want to sketch the lines. Do they appear perpendicular?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836610994\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836310492\">\n<div data-type=\"problem\" id=\"fs-id1167836415129\">\n<p id=\"fs-id1167836700045\">Find an equation of a line that is perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0e3ca3f6eb8810e090b4ceee7f6e129b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bfbe01e682dc0a32c559a939c4aa54e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833379801\">\n<p id=\"fs-id1167836515773\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829786398\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836594788\">\n<div data-type=\"problem\" id=\"fs-id1167826205784\">\n<p id=\"fs-id1167829691675\">Find an equation of a line that is perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ee7bf59b42611ad4534a6d8ca47648e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"55\" style=\"vertical-align: -4px;\" \/> that contains the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e6b256c75410cb8b2e66b0a1a24236d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/> Write the equation in slope-intercept form.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829748611\">\n<p id=\"fs-id1167836612514\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b3dc975a98ccada6f136856736d7df06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833202337\" class=\"media-2\">\n<p id=\"fs-id1167836554915\">Access these online resources for additional instruction and practice with finding the equation of a line.<\/p>\n<ul id=\"fs-id1167836558410\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/37slopeycept\">Write an Equation of Line Given its slope and Y-Intercept<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/37slopepoint\">Using Point Slope Form to Write the Equation of a Line, Find the equation given slope and point<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/37twoptspline\">Find the equation given two points<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/37perpenpara\">Find the equation of perpendicular and parallel lines<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836539487\">\n<h3 data-type=\"title\">Key Concepts<\/h3>\n<ul id=\"fs-id1167833290521\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">How to find an equation of a line given the slope and a point.<\/strong>\n<ol id=\"fs-id1167829746878\" type=\"1\" class=\"stepwise\">\n<li>Identify the slope.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Write the equation in slope-intercept form.\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">How to find an equation of a line given two points.<\/strong>\n<ol id=\"fs-id1167836516510\" type=\"1\" class=\"stepwise\">\n<li>Find the slope using the given points. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e8828e33f8f597c9b3df95aa3a0786c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#95;&#123;&#50;&#125;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#125;&#123;&#123;&#120;&#125;&#95;&#123;&#50;&#125;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"81\" style=\"vertical-align: -9px;\" \/><\/li>\n<li>Choose one point.<\/li>\n<li>Substitute the values into the point-slope form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Write the equation in slope-intercept form.\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167829579861\" class=\"unnumbered\" summary=\"The table is titled To Write and Equation of a Line. It has three columns labeled \u201cIf given,\u201d \u201cUse,\u201d, and \u201cForm.\u201d The first row shows that if the slope and y intercept are given, use the slope-intercept form, which is y equals mx plus b. The second row shows that if the slope and a point are given, use the point-slope form, which is y minus y sub 1 equals m times the quantity x minus x sub 1.\">\n<thead>\n<tr>\n<th colspan=\"3\" data-valign=\"middle\" data-align=\"center\">To Write an Equation of a Line<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">If given:<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">Use:<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">Form:<\/strong><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Slope and <em data-effect=\"italics\">y<\/em>-intercept<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">slope-intercept<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec94fd0d8ebcb10f78d886544058548e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Slope and a point<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">point-slope<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">Two points<\/td>\n<td data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">point-slope<\/strong><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">How to find an equation of a line parallel to a given line.<\/strong>\n<ol id=\"fs-id1167836325992\" type=\"1\" class=\"stepwise\">\n<li>Find the slope of the given line.<\/li>\n<li>Find the slope of the parallel line.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Write the equation in slope-intercept form<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">How to find an equation of a line perpendicular to a given line.<\/strong>\n<ol id=\"fs-id1167836287222\" type=\"1\" class=\"stepwise\">\n<li>Find the slope of the given line.<\/li>\n<li>Find the slope of the perpendicular line.<\/li>\n<li>Identify the point.<\/li>\n<li>Substitute the values into the point-slope form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-164cc8baf3c63433c4ff95b52af31e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>Write the equation in slope-intercept form.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836706806\">\n<div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167829589591\">\n<h4 data-type=\"title\">Practice Makes Perfect<\/h4>\n<p id=\"fs-id1167836715608\"><strong data-effect=\"bold\">Find an Equation of the Line Given the Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/strong><\/p>\n<p id=\"fs-id1167836415908\">In the following exercises, find the equation of a line with given slope and <em data-effect=\"italics\">y<\/em>-intercept. Write the equation in slope-intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829753548\">\n<div data-type=\"problem\" id=\"fs-id1167829714595\">\n<p id=\"fs-id1167836319403\">slope 3 and<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829695346\">\n<p id=\"fs-id1167829749967\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b3640b20491417f9f770b0d87917fd24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826097524\">\n<div data-type=\"problem\" id=\"fs-id1167833051126\">\n<p id=\"fs-id1167833240421\">slope 8 and<\/p>\n<div data-type=\"newline\"><\/div>\n<p><em data-effect=\"italics\">y<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-76ba30a779b2946f1d9c14bf4ce7c710_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829579132\">\n<div data-type=\"problem\" id=\"fs-id1167826205064\">\n<p id=\"fs-id1167833310065\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833379389\">\n<p id=\"fs-id1167836558333\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-64c61b5034010d35abb6efee026ea5bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829810647\">\n<div data-type=\"problem\" id=\"fs-id1167829906500\">\n<p id=\"fs-id1167836547898\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> and<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836387436\">\n<div data-type=\"problem\" id=\"fs-id1167836349166\">\n<p id=\"fs-id1167833056712\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e174a73678f6bd6f70d7aaec8f911349_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> and<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5f6ab1a0ed415088c10eaaa3977a4992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836551668\">\n<p id=\"fs-id1167829715758\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-31c3a332e84de5f26efdd3b93c76dac1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824767097\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836561278\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aa266d939635a899a53c3c9df44a7ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/> and<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829712261\">\n<div data-type=\"problem\" id=\"fs-id1167836447386\">\n<p id=\"fs-id1167836626157\">slope 0 and<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836456484\">\n<p id=\"fs-id1167836287662\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9f371b4e77462e28d9f6119571c92982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829711770\">\n<div data-type=\"problem\" id=\"fs-id1167836432947\">\n<p id=\"fs-id1167829921553\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> and<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1167833059421\">In the following exercises, find the equation of the line shown in each graph. Write the equation in slope-intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836544522\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836626384\">\n<p id=\"fs-id1167833271997\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833271998\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 5), (1, negative 2), and (2, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_201_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 5), (1, negative 2), and (2, 1).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829598941\">\n<p id=\"fs-id1167829853948\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-47bdbf719e41e4cd61a7a609f53c9186_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833349591\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836507156\">\n<p id=\"fs-id1167836288754\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836288755\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 4), (1, 2), and (2, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_202_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 4), (1, 2), and (2, 0).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836440491\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829580573\">\n<p id=\"fs-id1167824839801\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167824839802\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (2, negative 2), and (6, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_203_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (2, negative 2), and (6, 0).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836550635\">\n<p id=\"fs-id1167836607064\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6b9d262703706430bfe9be960d499e29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833361650\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167832936934\">\n<p id=\"fs-id1167833256684\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836520071\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (4, 5), and (8, 8).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_204_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (4, 5), and (8, 8).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836417359\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833128976\">\n<p id=\"fs-id1167833018360\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833018362\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 3), (3, negative 1), and (6, negative 5).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_205_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 3), (3, negative 1), and (6, negative 5).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167826177601\">\n<p id=\"fs-id1167836613599\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aa782b9f7087c2644cc29dd787d89de5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836485683\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829597028\">\n<p id=\"fs-id1167832927168\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833050769\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 1), (2, negative 4), and (4, negative 7).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_206_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 1), (2, negative 4), and (4, negative 7).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833274590\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829811991\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836321761\" data-alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_207_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829754778\">\n<p id=\"fs-id1167836429456\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f986dbfac9d3f29a18cba91e9efa9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836609306\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167832976669\">\n<p id=\"fs-id1167833339044\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833339046\" data-alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 6), (1, 6), and (2, 6).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_208_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 6), (1, 6), and (2, 6).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167836529707\"><strong data-effect=\"bold\">Find an Equation of the Line Given the Slope and a Point<\/strong><\/p>\n<p id=\"fs-id1167833380664\">In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833407507\">\n<div data-type=\"problem\" id=\"fs-id1167836731148\">\n<p id=\"fs-id1167829681166\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f19c5674ae6dd08ae61f60303f9606e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-38f47676ff4305b6e1df48d364862ed0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829783810\">\n<p id=\"fs-id1167836558580\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e886ab8762bb6e5eb0de107dd905f7d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833047536\">\n<div data-type=\"problem\" id=\"fs-id1167836615924\">\n<p id=\"fs-id1167836792953\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b4888d869e1155af607a763623122de0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-27acd60b4851baa3fac77a6a37f24296_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836509627\">\n<div data-type=\"problem\" id=\"fs-id1167829594543\">\n<p id=\"fs-id1167824737321\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5991736f7ec3a9a12f1815521970e7d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-064fbe5b13d7774ef232dcf1aebc3fa5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829720125\">\n<p id=\"fs-id1167836688498\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f139e4c1029ae94acd19b16b22fe685a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829811645\">\n<div data-type=\"problem\" id=\"fs-id1167836363112\">\n<p id=\"fs-id1167829751544\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-31f9f5e0c30ce6e4e9018dba6ba129f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8781692f7fffdf9ddfd97a6c49cb6935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826077523\">\n<div data-type=\"problem\" id=\"fs-id1167829749598\">\n<p id=\"fs-id1167829689340\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6d64e7debd949a16d05765e2463a5f45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ebe785a1a1f173c2cb47dc17a15cdc63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829599864\">\n<p id=\"fs-id1167836561099\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-912a1403d7554d5777364a8f77e9c2a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836699450\">\n<div data-type=\"problem\" id=\"fs-id1167824732204\">\n<p id=\"fs-id1167824773429\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1610fe4d7f24d08ed646c83787554e92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0079e38fdd16e43ef7a238df2ab245d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833269887\">\n<div data-type=\"problem\" id=\"fs-id1167836729979\">\n<p id=\"fs-id1167836729981\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7670b37d1e4f1ca32ea0ecb4de1b2177_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#55;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-659f5d2dee5bcea4b83fdb4d330c9b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836610073\">\n<p id=\"fs-id1167836610075\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b6b0038ca138291354ec7b88d33ba9a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#55;&#120;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833056175\">\n<div data-type=\"problem\" id=\"fs-id1167836510358\">\n<p id=\"fs-id1167836576450\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-45ac209879cfebf74e4dfaab6e07433d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#52;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e6b25c6279fe53efe7c78796a156eeed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829597969\">\n<div data-type=\"problem\" id=\"fs-id1167829597972\">\n<p id=\"fs-id1167836567138\">Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-edd8d8b57c2815309edbd447803c95fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829754568\">\n<p id=\"fs-id1167829785045\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-39af43abd99adaf051fde7775af522c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836495293\">\n<div data-type=\"problem\" id=\"fs-id1167836495295\">\n<p id=\"fs-id1167829620386\">Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e6b25c6279fe53efe7c78796a156eeed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826083425\">\n<div data-type=\"problem\" id=\"fs-id1167826083427\">\n<p id=\"fs-id1167829905739\">Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6eb713a032efe6d2cd357cc2ab12b55a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833379180\">\n<p id=\"fs-id1167836602221\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c15f100d859ec9077a43994ca473b018_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829620802\">\n<div data-type=\"problem\" id=\"fs-id1167829620804\">\n<p id=\"fs-id1167824740609\">Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-22807f5b7dd745b2825d8e7373202547_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833303310\"><strong data-effect=\"bold\">Find an Equation of the Line Given Two Points<\/strong><\/p>\n<p id=\"fs-id1167829651567\">In the following exercises, find the equation of a line containing the given points. Write the equation in slope-intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829880329\">\n<div data-type=\"problem\" id=\"fs-id1167829880331\">\n<p id=\"fs-id1167836518535\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-80be894898c77ffda9d4d5843e6791f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-159ccfbcee3ed270fafd4d79974b76e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836543899\">\n<p id=\"fs-id1167836543902\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8a1bb5f3376f9b2672f83545d4390c7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832940554\">\n<div data-type=\"problem\" id=\"fs-id1167829691245\">\n<p id=\"fs-id1167836689328\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1804935101b0791adf13cb00d6ac306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9eb44641a2132855d0bc4176e9a177ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836526101\">\n<div data-type=\"problem\" id=\"fs-id1167836526103\">\n<p id=\"fs-id1167836792213\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9523da542e5bfc81814e047c926984c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-09b8f562525976b9372e834320b90059_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836292965\">\n<p id=\"fs-id1167829595244\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8d73397bafc27d972aef8bb2237a3be8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"91\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829597670\">\n<div data-type=\"problem\" id=\"fs-id1167833356319\">\n<p id=\"fs-id1167833329138\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eb242707b07d2123762ae0b5253ad3ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9df6f11c9acd485fc6217b8d99af97d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833311141\">\n<div data-type=\"problem\" id=\"fs-id1167833311143\">\n<p id=\"fs-id1167836415243\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f2347704000ad2e9ae878a8427611b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0f601729b3265a543d4d2c806c93a73f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#44;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829756066\">\n<p id=\"fs-id1167824764624\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1e76a4b2f2378c28d47bf2578fc08203_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829726391\">\n<div data-type=\"problem\" id=\"fs-id1167832982215\">\n<p id=\"fs-id1167832982217\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c1c6d0c0591d57104498832e4e3a741a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1ae14577219b56870e499fe73480515a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833009732\">\n<div data-type=\"problem\" id=\"fs-id1167829753956\">\n<p id=\"fs-id1167836506442\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e2c3a69d33f9737210f9c4f1551f4b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bb76d278ef8bf9c035a41ef898b53f04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167824617257\">\n<p id=\"fs-id1167833076770\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aa18e3e501ae50d4deff8b260e3f1a84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#50;&#125;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824737272\">\n<div data-type=\"problem\" id=\"fs-id1167836434306\">\n<p id=\"fs-id1167829786961\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a13cc40f70d7b9c3ffc642dcd389fa6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836524732\">\n<div data-type=\"problem\" id=\"fs-id1167836524735\">\n<p id=\"fs-id1167825702449\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5f3a1814d4c4364566cfa9f7341421fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f29397311f66a76c062ac88ea3db09b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826131285\">\n<p id=\"fs-id1167826131287\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-49af7f686347e06977fd3a18757933db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836322984\">\n<div data-type=\"problem\" id=\"fs-id1167836418558\">\n<p id=\"fs-id1167836418560\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a4ee5cb7ef0ccc3c03dfedce09fb6342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829894553\">\n<div data-type=\"problem\" id=\"fs-id1167826206606\">\n<p id=\"fs-id1167826206608\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-abcb6ace4b542ff0928998579e86da44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec1f58e3551111ede13ce2158eff570f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167824607152\">\n<p id=\"fs-id1167824607154\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824590416\">\n<div data-type=\"problem\" id=\"fs-id1167833309132\">\n<p id=\"fs-id1167833309135\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a7b90c027eccd1d5f6de21196682699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-659f5d2dee5bcea4b83fdb4d330c9b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836756855\"><strong data-effect=\"bold\">Find an Equation of a Line Parallel to a Given Line<\/strong><\/p>\n<p id=\"fs-id1167836738196\">In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836567374\">\n<div data-type=\"problem\" id=\"fs-id1167829893821\">\n<p id=\"fs-id1167829893823\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-341a8015b8ee724b31fc6984616240b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#43;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ce830c2dfa3b70e2906cf4d1b7248973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167832945777\">\n<p id=\"fs-id1167833272217\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d76269f8d9b324873c9b8e3993ef6892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836598894\">\n<div data-type=\"problem\" id=\"fs-id1167829741274\">\n<p id=\"fs-id1167829741276\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-330c4b2e4f9d8057c3b7bebefe4f2448_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#45;&#49;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bb76d278ef8bf9c035a41ef898b53f04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836787998\">\n<div data-type=\"problem\" id=\"fs-id1167829810536\">\n<p id=\"fs-id1167829810538\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7e46be096cb6d83b5627a6ef86948f3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#121;&#61;&#54;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc6a40acab1fcbe9adecd900d5d2a756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833382488\">\n<p id=\"fs-id1167833382490\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fe73296a6eb057f3b8df5137955f8bdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829749845\">\n<div data-type=\"problem\" id=\"fs-id1167829749847\">\n<p id=\"fs-id1167836596678\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5a1aca9e1cb602ef57f7ac31aeac1cb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#54;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7bbcc10c2ea6e8df46d70e4728304a94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833019832\">\n<div data-type=\"problem\" id=\"fs-id1167833019834\">\n<p id=\"fs-id1167836717185\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-50c730f9beb24b96c2e61fc8f3b92726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-37fa9dbb8454d162ef24836afb0c0bf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833058199\">\n<p id=\"fs-id1167829624480\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836486058\">\n<div data-type=\"problem\" id=\"fs-id1167836486060\">\n<p id=\"fs-id1167836531943\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2fb7c08bc2cb09e340e3bac4c907f908_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#50;&#61;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"77\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a685e6a8556e8135bece1243dc70fe1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836391229\">\n<div data-type=\"problem\" id=\"fs-id1167836391231\">\n<p id=\"fs-id1167829619310\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9be3cc2e6f8a54fc883e8cbea6cf7c83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8fbb5d034d8bc7481119846ba5facddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836609836\">\n<p id=\"fs-id1167836609838\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f986dbfac9d3f29a18cba91e9efa9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829811153\">\n<div data-type=\"problem\" id=\"fs-id1167824590420\">\n<p id=\"fs-id1167824590422\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-11278bbccb3813cee6393fad36b93b5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#50;&#61;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"76\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f054d79e93ab302f68adcad7d4c3ec21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1167829621585\"><strong data-effect=\"bold\">Find an Equation of a Line Perpendicular to a Given Line<\/strong><\/p>\n<p id=\"fs-id1167836526732\">In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829752070\">\n<div data-type=\"problem\" id=\"fs-id1167833361655\">\n<p id=\"fs-id1167833361658\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bae29625e51ee30e0941604d7a168813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#43;&#51;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f78f604644c2cdddbea2fc4d8ad49cca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833047531\">\n<p id=\"fs-id1167836417222\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-755037b7c634e8f6760f24bebd6f5a2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836608786\">\n<div data-type=\"problem\" id=\"fs-id1167836608788\">\n<p id=\"fs-id1167829923321\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cc282db41295038ead1435a40b67ef86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;&#43;&#53;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c4a2258b08828b82f5478b79177f57c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836701461\">\n<div data-type=\"problem\" id=\"fs-id1167836732331\">\n<p id=\"fs-id1167836732333\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4d7ea0f29c57b947cfe0d917aa06d021_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-862a9525ac8db19009bf877fff4597b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836312930\">\n<p id=\"fs-id1167829744039\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e2498cd0b8a27adb0965b5a492fd4b3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836613635\">\n<div data-type=\"problem\" id=\"fs-id1167829596047\">\n<p id=\"fs-id1167829596049\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-61870c0df3b7092f8e34e17103c593f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#52;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6d5b80bc57d91ba9e2936cc72d75618b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836612285\">\n<div data-type=\"problem\" id=\"fs-id1167829787371\">\n<p id=\"fs-id1167829787373\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-559aa103cb2898e4933e39f9447eca70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#51;&#121;&#61;&#56;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6de38faced02869069c306c45a22c5e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829693456\">\n<p id=\"fs-id1167836731791\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-025571680eb287dec5e30e6cab19ad77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832977098\">\n<div data-type=\"problem\" id=\"fs-id1167832977101\">\n<p id=\"fs-id1167833175512\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fcfed0a7d6d1a1fb41d26a218a7d7256_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#53;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1f307aa6b65fb69739e6c2b7458409de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836518806\">\n<div data-type=\"problem\" id=\"fs-id1167836518808\">\n<p id=\"fs-id1167824735838\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ef83983b45988ff4d0145e381bab37e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#53;&#121;&#61;&#54;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836439631\">\n<p id=\"fs-id1167836567424\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-de6f4c1a9034dd7da347981bd84961dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829908672\">\n<div data-type=\"problem\" id=\"fs-id1167829908674\">\n<p id=\"fs-id1167829714449\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3f24c7e0ec2cd14945710380df4fe884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#53;&#121;&#61;&#45;&#51;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830059063\">\n<div data-type=\"problem\" id=\"fs-id1167830059065\">\n<p id=\"fs-id1167822966262\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c7d62a78a97a33b2bfba1ddcfe9dbb8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aecc845ff8fcecb422091e6436adca8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833361699\">\n<p id=\"fs-id1167833361701\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0621c4f761e7864714642fcc62d4c42f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836496973\">\n<div data-type=\"problem\" id=\"fs-id1167829745657\">\n<p id=\"fs-id1167829745659\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f0fdc1717d47916064f25e11eb18b433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a685e6a8556e8135bece1243dc70fe1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836729396\">\n<div data-type=\"problem\" id=\"fs-id1167836729398\">\n<p id=\"fs-id1167826077209\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e6630248d786d4a1203d75f9f6b44236_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#55;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9523da542e5bfc81814e047c926984c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833059151\">\n<p id=\"fs-id1167833082323\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836327353\">\n<div data-type=\"problem\" id=\"fs-id1167826205702\">\n<p id=\"fs-id1167826205704\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-788573bc8e8d02a50d95d598dd96420f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-91357ad9f837f690ca370a0ee126647e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836538674\">\n<div data-type=\"problem\" id=\"fs-id1167836538676\">\n<p id=\"fs-id1167836538678\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-88589d91cd9c427fec349a3594f2eb02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#51;&#61;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"76\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ecc91b8d5e91ea23c08fcf2ee52342c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833008898\">\n<p id=\"fs-id1167833008900\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826130658\">\n<div data-type=\"problem\" id=\"fs-id1167826130660\">\n<p id=\"fs-id1167833369088\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1ed58d09796311e6e10c1a422e04ded1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#54;&#61;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"76\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eb242707b07d2123762ae0b5253ad3ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829807550\">\n<div data-type=\"problem\" id=\"fs-id1167829807552\">\n<p id=\"fs-id1167836611143\">line <em data-effect=\"italics\">y<\/em>-axis,<\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aecc845ff8fcecb422091e6436adca8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836598022\">\n<p id=\"fs-id1167836598024\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0621c4f761e7864714642fcc62d4c42f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836389046\">\n<div data-type=\"problem\" id=\"fs-id1167836389048\">\n<p id=\"fs-id1167833274080\">line <em data-effect=\"italics\">y<\/em>-axis,<\/p>\n<div data-type=\"newline\"><\/div>\n<p>point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bb160c5e6177bdd7a1d220c410258e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1171791101176\"><strong data-effect=\"bold\">Mixed Practice<\/strong><\/p>\n<p id=\"fs-id1167832977157\">In the following exercises, find the equation of each line. Write the equation in slope-intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829879476\">\n<div data-type=\"problem\" id=\"fs-id1167829879478\">\n<p id=\"fs-id1167829879480\">Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1804935101b0791adf13cb00d6ac306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9eb44641a2132855d0bc4176e9a177ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836728415\">\n<p id=\"fs-id1167836728417\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5bf9c46f23b6ce4490dd85912017c7b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830123660\">\n<div data-type=\"problem\" id=\"fs-id1167830123662\">\n<p id=\"fs-id1167836728914\">Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dd6f8f312ab67ad0422a4959540654f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a17ffffadfb8456567f4803e943d15a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829624584\">\n<div data-type=\"problem\" id=\"fs-id1167833061186\">\n<p id=\"fs-id1167833061188\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f07549c44a9434d3879a4cd172be2503_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/> containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc9db18ceda8b325515059e9c425b44f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833061247\">\n<p id=\"fs-id1167833061249\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cb1fb0fbe8cc3185cd9b01efdaf3c98a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833049256\">\n<div data-type=\"problem\" id=\"fs-id1167836507510\">\n<p id=\"fs-id1167836507512\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b4888d869e1155af607a763623122de0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/> containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-27acd60b4851baa3fac77a6a37f24296_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836533232\">\n<div data-type=\"problem\" id=\"fs-id1167836533234\">\n<p id=\"fs-id1167833338169\">Parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4b4e1ff0cfff58834ab101139f9c0f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#121;&#61;&#54;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/> containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833047237\">\n<p id=\"fs-id1167833047239\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-de999b976bd2d001a0649a56d2434459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836664674\">\n<div data-type=\"problem\" id=\"fs-id1167836664676\">\n<p id=\"fs-id1167836476792\">Parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5a1aca9e1cb602ef57f7ac31aeac1cb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#54;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/> containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836714016\">\n<div data-type=\"problem\" id=\"fs-id1167836714018\">\n<p id=\"fs-id1167829849933\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-31f9f5e0c30ce6e4e9018dba6ba129f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8781692f7fffdf9ddfd97a6c49cb6935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829696829\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f021b61c6b167f02773bd3a54482a16a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829720221\">\n<div data-type=\"problem\" id=\"fs-id1167829579270\">\n<p id=\"fs-id1167829579272\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5991736f7ec3a9a12f1815521970e7d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-064fbe5b13d7774ef232dcf1aebc3fa5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833128553\">\n<div data-type=\"problem\" id=\"fs-id1167833128555\">\n<p id=\"fs-id1167833128557\">Perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-de9588c0ad0d46a95c687e61a8bd4dac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#49;&#61;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"76\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b61914c33c0ffe75331208eaa502d627_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836596745\">\n<p id=\"fs-id1167836596747\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833339135\">\n<div data-type=\"problem\" id=\"fs-id1167833339137\">\n<p id=\"fs-id1167829590713\">Perpendicular to the line <em data-effect=\"italics\">y<\/em>-axis, point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-551477e8eec13715fc061945ccc1b984_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836756601\">\n<div data-type=\"problem\" id=\"fs-id1167836756604\">\n<p id=\"fs-id1167836756606\">Parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-09bee320bf56e1f1abb3aeb986256f0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -4px;\" \/> containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ef9b0ead245d0b508218b1cb59d48442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829787446\">\n<p id=\"fs-id1167836572789\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167825986925\">\n<div data-type=\"problem\" id=\"fs-id1167825986927\">\n<p id=\"fs-id1167825986929\">Parallel to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-50c730f9beb24b96c2e61fc8f3b92726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -4px;\" \/> containing point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0bd0b31c672d6277d527b16652fb255d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829931362\">\n<div data-type=\"problem\" id=\"fs-id1167832951124\">\n<p id=\"fs-id1167832951126\">Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9523da542e5bfc81814e047c926984c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c02ba61efe13be423bc75f83a9846930_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833366682\">\n<p id=\"fs-id1167833366684\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-377943fff2146f505c6b3032b78a5e28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836309284\">\n<div data-type=\"problem\" id=\"fs-id1167829787935\">\n<p id=\"fs-id1167829787938\">Containing the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eb242707b07d2123762ae0b5253ad3ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-84e35e40e916e50503f09b25572279f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833407736\">\n<div data-type=\"problem\" id=\"fs-id1167836673451\">\n<p id=\"fs-id1167836673453\">Perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a59441b40f8fa335993f97970784e824_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#50;&#121;&#61;&#53;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-627391f2fad7216057fc57692a374893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833345909\">\n<p id=\"fs-id1167833345912\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-767f43f1e81a6336edff3fd764081f28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836623550\">\n<div data-type=\"problem\" id=\"fs-id1167836518250\">\n<p id=\"fs-id1167836518252\">Perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9bf6d1e8ec48bf4e30b1c9e22d3d8425_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#121;&#61;&#49;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"writing\" data-depth=\"2\" id=\"fs-id1167836690259\">\n<h4 data-type=\"title\">Writing Exercises<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1167824976247\">\n<div data-type=\"problem\" id=\"fs-id1167836600645\">\n<p id=\"fs-id1167836600647\">Why are all horizontal lines parallel?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836363428\">\n<p id=\"fs-id1167836363430\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836484625\">\n<div data-type=\"problem\" id=\"fs-id1167836484628\">\n<p id=\"fs-id1167836362164\">Explain in your own words why the slopes of two perpendicular lines must have opposite signs.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167824732320\">\n<h4 data-type=\"title\">Self Check<\/h4>\n<p id=\"fs-id1167824732325\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167824648924\" data-alt=\"The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is \u201cconfidently\u201d, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cfind the equation of the line given the slope and y-intercept\u201d, \u201cfind an equation of the line given the slope and a point\u201d, \u201cfind an equation of the line given two points\u201d, \u201cfind an equation of a line parallel to a given line\u201d, and \u201cfind an equation of a line perpendicular to a given line\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_03_03_209_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is \u201cconfidently\u201d, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cfind the equation of the line given the slope and y-intercept\u201d, \u201cfind an equation of the line given the slope and a point\u201d, \u201cfind an equation of the line given two points\u201d, \u201cfind an equation of a line parallel to a given line\u201d, and \u201cfind an equation of a line perpendicular to a given line\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.\" \/><\/span><\/p>\n<p id=\"fs-id1167829748644\"><span class=\"token\">\u24d1<\/span> What does this checklist tell you about your mastery of this section? What steps will you take to improve?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h3 data-type=\"glossary-title\">Glossary<\/h3>\n<dl id=\"fs-id1167836545346\">\n<dt>point-slope form<\/dt>\n<dd id=\"fs-id1167836545350\">The point-slope form of an equation of a line with slope <em data-effect=\"italics\">m<\/em> and containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-daf7d3000a611d6a6b02b6093c3dfb1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#44;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -4px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a6552ba3ed5b1b576806c08bdec6354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#123;&#121;&#125;&#95;&#123;&#49;&#125;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#123;&#120;&#125;&#95;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":103,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1866","chapter","type-chapter","status-publish","hentry"],"part":1643,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1866","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":0,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1866\/revisions"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/parts\/1643"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1866\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/media?parent=1866"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapter-type?post=1866"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/contributor?post=1866"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/license?post=1866"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}