{"id":1525,"date":"2021-05-19T16:44:49","date_gmt":"2021-05-19T16:44:49","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/graph-review\/"},"modified":"2022-04-30T21:27:10","modified_gmt":"2022-04-30T21:27:10","slug":"graph-review","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/graph-review\/","title":{"raw":"4.7 Chapter Review","rendered":"4.7 Chapter Review"},"content":{"raw":"[latexpage]\r\n

Review Exercises<\/h1>\r\n

Plot Points in a Rectangular Coordinate System<\/h2>\r\n

In the following exercises, plot each point in a rectangular coordinate system.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
1.\r\na) \\(\\left(4,3\\right)\\)\r\nb) \\(\\left(-4,3\\right)\\)\r\nc) \\(\\left(-4,-3\\right)\\)\r\nd) \\(\\left(4,-3\\right)\\)<\/td>\r\n2.\r\na) \\(\\left(-1,-5\\right)\\)\r\nb) \\(\\left(-3,4\\right)\\)\r\nc) \\(\\left(2,-3\\right)\\)\r\nd) \\(\\left(1,\\frac{5}{2}\\right)\\)<\/td>\r\n<\/tr>\r\n
3.\r\na) \\(\\left(2,\\frac{3}{2}\\right)\\)\r\nb) \\(\\left(3,\\frac{4}{3}\\right)\\)\r\nc) \\(\\left(\\frac{1}{3},-4\\right)\\)\r\nd) \\(\\left(\\frac{1}{2},-5\\right)\\)<\/td>\r\n4.\r\na) \\(\\left(-2,0\\right)\\)\r\nb) \\(\\left(0,-4\\right)\\)\r\nc) \\(\\left(0,5\\right)\\)\r\nd) \\(\\left(3,0\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Identify Points on a Graph<\/h2>\r\n

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.<\/p>\r\n\r\n\r\n\r\n\r\n
5.\"The<\/span><\/span><\/td>\r\n6.\"The<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Verify Solutions to an Equation in Two Variables<\/h2>\r\n

In the following exercises, which ordered pairs are solutions to the given equations?<\/p>\r\n\r\n\r\n\r\n\r\n
\r\n

7. \\(y=6x-2\\)<\/p>\r\n

a) \\(\\left(1,4\\right)\\)\r\nb) \\(\\left(\\frac{1}{3},0\\right)\\)\r\nc) \\(\\left(6,-2\\right)\\)<\/p>\r\n<\/td>\r\n

\r\n

8. \\(5x+y=10\\)<\/p>\r\n

a) \\(\\left(5,1\\right)\\)\r\nb) \\(\\left(2,0\\right)\\)\r\nc) \\(\\left(4,-10\\right)\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Complete a Table of Solutions to a Linear Equation in Two Variables<\/h2>\r\n

In the following exercises, complete the table to find solutions to each linear equation.<\/p>\r\n\r\n\r\n\r\n\r\n
\r\n

9. \\(y=-\\frac{1}{2}x+3\\)<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\\(x\\)<\/strong><\/td>\r\n\\(y\\)<\/strong><\/td>\r\n\\(\\left(x,y\\right)\\)<\/strong><\/td>\r\n<\/tr>\r\n
0<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\\(-2\\)<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/td>\r\n\r\n

10. \\(y=4x-1\\)<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\\(x\\)<\/strong><\/td>\r\n\\(y\\)<\/strong><\/td>\r\n\\(\\left(x,y\\right)\\)<\/strong><\/td>\r\n<\/tr>\r\n
\\(0\\)<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\\(1\\)<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\\(-2\\)<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/td>\r\n<\/tr>\r\n
\r\n

11. \\(3x+2y=6\\)<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\\(x\\)<\/td>\r\n\\(y\\)<\/td>\r\n\\(\\left(x,y\\right)\\)<\/td>\r\n<\/tr>\r\n
0<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n0<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\\(-2\\)<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/td>\r\n\r\n

12. \\(x+2y=5\\)<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\\(x\\)<\/strong><\/td>\r\n\\(y\\)<\/strong><\/td>\r\n\\(\\left(x,y\\right)\\)<\/strong><\/td>\r\n<\/tr>\r\n
<\/td>\r\n0<\/td>\r\n<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
\\(-1\\)<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Find Solutions to a Linear Equation in Two Variables<\/h2>\r\n

In the following exercises, find three solutions to each linear equation.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
13. \\(x+y=-4\\)<\/td>\r\n14. \\(x+y=3\\)<\/td>\r\n<\/tr>\r\n
15. \\(y=\\text{-}x-1\\)<\/td>\r\n16. \\(y=3x+1\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Recognize the Relation Between the Solutions of an Equation and its Graph<\/h2>\r\n

In the following exercises, for each ordered pair, decide:<\/p>\r\na) Is the ordered pair a solution to the equation?\r\n\r\nb) Is the point on the line?\r\n\r\n\r\n\r\n
17.\r\n

\\(y=\\frac{2}{3}x-1\\)<\/p>\r\n

\\(\\left(0,-1\\right)\\) (3, 1)<\/p>\r\n

\\(\\left(-3,-3\\right)\\) (6, 4)<\/p>\r\n\"The<\/span><\/td>\r\n

18.\r\n

\\(y=\\text{-}x+4\\)<\/p>\r\n

\\(\\left(0,4\\right)\\)\\(\\left(-1,3\\right)\\)<\/p>\r\n

\\(\\left(2,2\\right)\\)\\(\\left(-2,6\\right)\\)<\/p>\r\n\"The<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Graph a Linear Equation by Plotting Points<\/h2>\r\n

In the following exercises, graph by plotting points.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
19. \\(y=-3x\\)<\/td>\r\n20. \\(y=4x-3\\)<\/td>\r\n<\/tr>\r\n
21. \\(x-y=6\\)<\/td>\r\n22. \\(y=\\frac{1}{2}x+3\\)<\/td>\r\n<\/tr>\r\n
23. \\(3x-2y=6\\)<\/td>\r\n24. \\(2x+y=7\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Graph Vertical and Horizontal lines<\/h2>\r\n

In the following exercises, graph each equation.<\/p>\r\n\r\n\r\n\r\n\r\n
25. \\(x=3\\)<\/td>\r\n26. \\(y=-2\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

In the following exercises, graph each pair of equations in the same rectangular coordinate system.<\/p>\r\n\r\n\r\n\r\n\r\n
27. \\(y=\\frac{4}{3}x\\) and \\(y=\\frac{4}{3}\\)<\/td>\r\n28. \\(y=-2x\\) and \\(y=-2\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Identify the x<\/em>- and y<\/em>-Intercepts on a Graph<\/h2>\r\n

In the following exercises, find the x<\/em>- and y<\/em>-intercepts.<\/p>\r\n\r\n\r\n\r\n\r\n
29.\"The<\/span><\/span><\/td>\r\n30. \"The<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Find the x<\/em>- and y<\/em>-Intercepts from an Equation of a Line<\/h2>\r\n

In the following exercises, find the intercepts of each equation.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
31. \\(x-y=-1\\)<\/td>\r\n32. \\(x+y=5\\)<\/td>\r\n<\/tr>\r\n
33. \\(2x+3y=12\\)<\/td>\r\n34. \\(x+2y=6\\)<\/td>\r\n<\/tr>\r\n
35. \\(y=3x\\)<\/td>\r\n36. \\(y=\\frac{3}{4}x-12\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Graph a Line Using the Intercepts<\/h2>\r\n

In the following exercises, graph using the intercepts.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
37. \\(-x+3y=3\\)<\/td>\r\n38. \\(x+y=-2\\)<\/td>\r\n<\/tr>\r\n
39. \\(x-y=4\\)<\/td>\r\n40. \\(2x-y=5\\)<\/td>\r\n<\/tr>\r\n
41. \\(2x-4y=8\\)<\/td>\r\n42. \\(y=2x\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Use Geoboards to Model Slope<\/h2>\r\n

In the following exercises, find the slope modeled on each geoboard.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
43. \"The<\/span><\/span><\/td>\r\n44. \"The<\/span><\/span><\/td>\r\n<\/tr>\r\n
45. \"The<\/span><\/span><\/td>\r\n46. \"The<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn the following exercises, model each slope. Draw a picture to show your results.\r\n\r\n\r\n\r\n\r\n
47. \\(\\frac{3}{2}\\)<\/td>\r\n48. \\(\\frac{1}{3}\\)<\/td>\r\n<\/tr>\r\n
49. \\(-\\frac{1}{2}\\)<\/td>\r\n50. \\(-\\frac{2}{3}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

In the following exercises, find the slope of each line shown. Use \\(m=\\frac{\\text{rise}}{\\text{run}}\\) to find the slope of a line from its graph.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
51. \"The<\/span><\/span><\/td>\r\n52. \"The<\/span><\/span><\/td>\r\n<\/tr>\r\n
53. \"The<\/span><\/span><\/td>\r\n54. \"\"<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Find the Slope of Horizontal and Vertical Lines<\/h2>\r\n

In the following exercises, find the slope of each line.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
55. \\(x=5\\)<\/td>\r\n56. \\(y=2\\)<\/td>\r\n<\/tr>\r\n
57. \\(y=-1\\)<\/td>\r\n58. \\(x=-3\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Use the Slope Formula to find the Slope of a Line between Two Points<\/h2>\r\n

In the following exercises, use the slope formula to find the slope of the line between each pair of points.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
59. \\(\\left(3,5\\right),\\left(4,-1\\right)\\)<\/td>\r\n60. \\(\\left(-1,-1\\right),\\left(0,5\\right)\\)<\/td>\r\n<\/tr>\r\n
61. \\(\\left(2,1\\right),\\left(4,6\\right)\\)<\/td>\r\n62. \\(\\left(-5,-2\\right),\\left(3,2\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Graph a Line Given a Point and the Slope<\/h2>\r\n

In the following exercises, graph each line with the given point and slope.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
63. \\(\\left(-3,4\\right)\\); \\(m=-\\frac{1}{3}\\)<\/td>\r\n64. \\(\\left(2,-2\\right)\\); \\(m=\\frac{5}{2}\\)<\/td>\r\n<\/tr>\r\n
65. y<\/em>-intercept 1; \\(m=-\\frac{3}{4}\\)<\/td>\r\n66. x<\/em>-intercept \\(-4\\); \\(m=3\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Solve Slope Applications<\/h2>\r\n

In the following exercises, solve these slope applications.<\/p>\r\n\r\n\r\n\r\n\r\n
67. A mountain road rises 50 feet for a 500-foot run. What is its slope? <\/span><\/td>\r\n68. The roof pictured below has a rise of 10 feet and a run of 15 feet. What is its slope?\r\n\"The<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Recognize the Relation Between the Graph and the Slope\u2013Intercept Form of an Equation of a Line<\/h2>\r\n

In the following exercises, use the graph to find the slope and y<\/em>-intercept of each line. Compare the values to the equation \\(y=mx+b\\).<\/p>\r\n\r\n\r\n\r\n\r\n
69.<\/span>\r\n\r\n\"The<\/span>\r\n

\\(y=-\\frac{2}{3}x+4\\)<\/p>\r\n<\/td>\r\n

70.<\/span>\r\n\r\n\"The<\/span>\r\n

\\(y=4x-1\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Identify the Slope and y-Intercept from an Equation of a Line<\/h2>\r\n

In the following exercises, identify the slope and y<\/em>-intercept of each line.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
71. \\(y=\\frac{5}{3}x-6\\)<\/td>\r\n72. \\(y=-4x+9\\)<\/td>\r\n<\/tr>\r\n
73. \\(4x-5y=8\\)<\/td>\r\n74. \\(5x+y=10\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Graph a Line Using Its Slope and Intercept<\/h2>\r\n

In the following exercises, graph the line of each equation using its slope and y<\/em>-intercept.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
75. \\(y=\\text{-}x-1\\)<\/td>\r\n76. \\(y=2x+3\\)<\/td>\r\n<\/tr>\r\n
77. \\(4x-3y=12\\)<\/td>\r\n78. \\(y=-\\frac{2}{5}x+3\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

In the following exercises, determine the most convenient method to graph each line.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
79. \\(y=-3\\)<\/td>\r\n80. \\(x=5\\)<\/td>\r\n<\/tr>\r\n
81. \\(x-y=2\\)<\/td>\r\n82. \\(2x+y=5\\)<\/td>\r\n<\/tr>\r\n
83. \\(y=\\frac{3}{4}x-1\\)<\/td>\r\n84. \\(y=x+2\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Graph and Interpret Applications of Slope\u2013Intercept<\/h2>\r\n\r\n\r\n\r\n
\r\n

85. Marjorie teaches piano. The equation \\(P=35h-250\\) models the relation between her weekly profit, P<\/em>, in dollars and the number of student lessons, s<\/em>, that she teaches.<\/p>\r\n\r\n

    \r\n \t
  1. Find Marjorie\u2019s profit for a week when she teaches no student lessons.<\/li>\r\n \t
  2. Find the profit for a week when she teaches 20 student lessons.<\/li>\r\n \t
  3. Interpret the slope and P<\/em>\u2013intercept of the equation.<\/li>\r\n \t
  4. Graph the equation.<\/li>\r\n<\/ol>\r\n<\/td>\r\n
\r\n

86. Katherine is a private chef. The equation \\(C=6.5m+42\\) models the relation between her weekly cost, C<\/em>, in dollars and the number of meals, m<\/em>, that she serves.<\/p>\r\n\r\n

    \r\n \t
  1. Find Katherine\u2019s cost for a week when she serves no meals.<\/li>\r\n \t
  2. Find the cost for a week when she serves 14 meals.<\/li>\r\n \t
  3. Interpret the slope and C<\/em>-intercept of the equation.<\/li>\r\n \t
  4. Graph the equation.<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Use Slopes to Identify Parallel Lines<\/h2>\r\n

    In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.<\/p>\r\n\r\n\r\n\r\n\r\n
    87. \\(2x-y=8;\\phantom{\\rule{0.2em}{0ex}}x-2y=4\\)<\/td>\r\n88. \\(4x-3y=-1;\\phantom{\\rule{0.2em}{0ex}}y=\\frac{4}{3}x-3\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Use Slopes to Identify Perpendicular Lines<\/h2>\r\n

    In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.<\/p>\r\n\r\n\r\n\r\n\r\n
    89. \\(3x-2y=5;2x+3y=6\\)<\/td>\r\n90. \\(y=5x-1;10x+2y=0\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Find an Equation of the Line Given the Slope and y<\/em>-Intercept<\/h2>\r\n

    In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope\u2013intercept form.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
    91. slope \\(-5\\) and \\(y\\text{-intercept}\\) \\(\\left(0,-3\\right)\\)<\/td>\r\n92. slope \\(\\frac{1}{3}\\) and \\(y\\text{-intercept}\\) \\(\\left(0,-6\\right)\\)<\/td>\r\n<\/tr>\r\n
    93. slope \\(-2\\) and \\(y\\text{-intercept}\\) \\(\\left(0,0\\right)\\)<\/td>\r\n94. slope \\(0\\) and \\(y\\text{-intercept}\\) \\(\\left(0,4\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    In the following exercises, find the equation of the line shown in each graph. Write the equation in slope\u2013intercept form.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
    95. \"The<\/span><\/span><\/td>\r\n96. \"The<\/span><\/span><\/td>\r\n<\/tr>\r\n
    97. \"The<\/span><\/span><\/td>\r\n98. \"The<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Find an Equation of the Line Given the Slope and a Point<\/h2>\r\n

    In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope\u2013intercept form.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
    99. \\(m=\\frac{3}{5}\\), point \\(\\left(10,6\\right)\\)<\/td>\r\n100. \\(m=-\\frac{1}{4}\\), point \\(\\left(-8,3\\right)\\)<\/td>\r\n<\/tr>\r\n
    101. \\(m=-2\\), point \\(\\left(-1,-3\\right)\\)<\/td>\r\n102. Horizontal line containing \\(\\left(-2,7\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Find an Equation of the Line Given Two Points<\/h2>\r\n

    In the following exercises, find the equation of a line containing the given points. Write the equation in slope\u2013intercept form.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
    103. \\(\\left(7,1\\right)\\) and \\(\\left(5,0\\right)\\)<\/td>\r\n104. \\(\\left(2,10\\right)\\) and \\(\\left(-2,-2\\right)\\)<\/td>\r\n<\/tr>\r\n
    105. \\(\\left(5,2\\right)\\) and \\(\\left(-1,2\\right)\\)<\/td>\r\n106. \\(\\left(3,8\\right)\\) and \\(\\left(3,-4\\right)\\).<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Find an Equation of a Line Parallel to a Given Line<\/h2>\r\n

    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\u2013intercept form.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
    107. line \\(2x+5y=-10\\), point \\(\\left(10,4\\right)\\)<\/td>\r\n108. line \\(y=-3x+6\\), point \\(\\left(1,-5\\right)\\)<\/td>\r\n<\/tr>\r\n
    109. line \\(y=-5\\), point \\(\\left(-4,3\\right)\\)<\/td>\r\n110. line \\(x=4\\), point \\(\\left(-2,-1\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Find an Equation of a Line Perpendicular to a Given Line<\/h2>\r\n

    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\u2013intercept form.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
    111. line \\(2x-3y=9\\), point \\(\\left(-4,0\\right)\\)<\/td>\r\n112. line \\(y=-\\frac{4}{5}x+2\\), point \\(\\left(8,9\\right)\\)<\/td>\r\n<\/tr>\r\n
    113. line \\(x=-5\\) point \\(\\left(2,1\\right)\\)<\/td>\r\n114. line \\(y=3\\), point \\(\\left(-1,-3\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Review Answers<\/h1>\r\n\r\n\r\n\r\n\r\n\r\n
    1. \"The<\/span><\/td>\r\n3. \"The<\/span><\/td>\r\n<\/tr>\r\n
    5. a) \\(\\left(2,0\\right)\\)\u2003b) \\(\\left(0,-5\\right)\\)\u2003c) \\(\\left(-4.0\\right)\\)\u2003d) \\(\\left(0,3\\right)\\)<\/td>\r\n7. a, b<\/td>\r\n<\/tr>\r\n
    9.\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(x\\)<\/strong><\/td>\r\n\\(y\\)<\/strong><\/td>\r\n\\(\\left(x,y\\right)\\)<\/strong><\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n3<\/td>\r\n\\(\\left(0,3\\right)\\)<\/td>\r\n<\/tr>\r\n
    4<\/td>\r\n1<\/td>\r\n(4, 1)<\/td>\r\n<\/tr>\r\n
    \\(-2\\)<\/td>\r\n4<\/td>\r\n\\(\\left(-2,4\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/td>\r\n11.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(x\\)<\/td>\r\n\\(y\\)<\/td>\r\n\\(\\left(x,y\\right)\\)<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n\\(-3\\)<\/td>\r\n\\(\\left(0,-3\\right)\\)<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n0<\/td>\r\n\\(\\left(2,0\\right)\\)<\/td>\r\n<\/tr>\r\n
    \\(-2\\)<\/td>\r\n\\(-6\\)<\/td>\r\n\\(\\left(-2,-6\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/td>\r\n<\/tr>\r\n
    13. Answers will vary.<\/td>\r\n15. Answers will vary.<\/td>\r\n<\/tr>\r\n
    17. a) yes; yes\u2003b) yes; no<\/td>\r\n19.\"The<\/span><\/td>\r\n<\/tr>\r\n
    21. \"The<\/span><\/td>\r\n23. \"The<\/span><\/td>\r\n<\/tr>\r\n
    25. \"The<\/span><\/td>\r\n27. \"The<\/span><\/td>\r\n<\/tr>\r\n
    29. \\(\\left(3,0\\right),\\left(0,3\\right)\\)<\/td>\r\n31. \\(\\left(-1,0\\right),\\left(0,1\\right)\\)<\/td>\r\n<\/tr>\r\n
    33. \\(\\left(6,0\\right),\\left(0,4\\right)\\)<\/td>\r\n35. \\(\\left(0,0\\right)\\)<\/td>\r\n<\/tr>\r\n
    37. \"Graph<\/a><\/td>\r\n39. \"Graph<\/a><\/td>\r\n<\/tr>\r\n
    41. \"graph<\/a><\/td>\r\n43. \\(\\frac{4}{3}\\)<\/td>\r\n<\/tr>\r\n
    45. \\(-\\frac{2}{3}\\)<\/td>\r\n47. \"The<\/span><\/td>\r\n<\/tr>\r\n
    49. \"The<\/span><\/td>\r\n51. 1<\/td>\r\n<\/tr>\r\n
    53. \\(-\\frac{1}{2}\\)<\/td>\r\n55. undefined<\/td>\r\n<\/tr>\r\n
    57. 0<\/td>\r\n59. \\(-6\\)<\/td>\r\n<\/tr>\r\n
    61. \\(\\frac{5}{2}\\)<\/td>\r\n63. \"The<\/span><\/td>\r\n<\/tr>\r\n
    65. \"The<\/span><\/td>\r\n67. \\(\\frac{1}{10}\\)<\/td>\r\n<\/tr>\r\n
    69. slope \\(m=-\\frac{2}{3}\\) and y<\/em>-intercept \\(\\left(0,4\\right)\\)<\/td>\r\n71. \\(\\frac{5}{3};\\left(0,-6\\right)\\)<\/td>\r\n<\/tr>\r\n
    73. \\(\\frac{4}{5};\\left(0,-\\frac{8}{5}\\right)\\)<\/td>\r\n75. \"The<\/span><\/td>\r\n<\/tr>\r\n
    77. \"The<\/span><\/td>\r\n79. horizontal line<\/td>\r\n<\/tr>\r\n
    81. intercepts<\/td>\r\n83. plotting points<\/td>\r\n<\/tr>\r\n
    85. a) \u2212250\u2003b) 450\u2003c) The slope, 35, means that Marjorie\u2019s weekly profit, P<\/em>, increases by \\$35 for each additional student lesson she teaches. The P<\/em>\u2013intercept means that when the number of lessons is 0, Marjorie loses \\$250.\u2003d)\r\n\"The<\/span><\/td>\r\n87. not parallel<\/td>\r\n<\/tr>\r\n
    89. perpendicular<\/td>\r\n91. \\(y=-5x-3\\)<\/td>\r\n<\/tr>\r\n
    93. \\(y=-2x\\)<\/td>\r\n95. \\(y=-3x+5\\)<\/td>\r\n<\/tr>\r\n
    97. \\(y=-4\\)<\/td>\r\n99. \\(y=\\frac{3}{5}x\\)<\/td>\r\n<\/tr>\r\n
    101. \\(y=-2x-5\\)<\/td>\r\n103. \\(y=\\frac{1}{2}x-\\frac{5}{2}\\)<\/td>\r\n<\/tr>\r\n
    105. \\(y=2\\)<\/td>\r\n107. \\(y=-\\frac{2}{5}x+8\\)<\/td>\r\n<\/tr>\r\n
    109. \\(y=3\\)<\/td>\r\n111. \\(y=-\\frac{3}{2}x-6\\)<\/td>\r\n<\/tr>\r\n
    113. \\(y=1\\)<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Practice Test<\/h1>\r\n\r\n\r\n\r\n\r\n
    1. Plot each point in a rectangular coordinate system.\r\n

    a) \\(\\left(2,5\\right)\\)\r\nb) \\(\\left(-1,-3\\right)\\)\r\nc) \\(\\left(0,2\\right)\\)\r\nd) \\(\\left(-4,\\frac{3}{2}\\right)\\)\r\ne) \\(\\left(5,0\\right)\\)<\/p>\r\n<\/td>\r\n

    		\r\n

    2. Which of the given ordered pairs are solutions to the equation \\(3x-y=6\\)?<\/p>\r\n

    a) \\(\\left(3,3\\right)\\)\r\nb) \\(\\left(2,0\\right)\\)\r\nc) \\(\\left(4,-6\\right)\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    3. Find three solutions to the linear equation \\(y=-2x-4\\).<\/td>\r\n4. Find the x<\/em>- and y<\/em>-intercepts of the equation \\(4x-3y=12\\).<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Find the slope of each line shown.<\/h2>\r\n\r\n\r\n\r\n\r\n
    5. \"The<\/span><\/td>\r\n6. \"The<\/span><\/td>\r\n<\/tr>\r\n
    7. \"The<\/span><\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n
    8. Find the slope of the line between the points \\(\\left(5,2\\right)\\) and \\(\\left(-1,-4\\right)\\).<\/td>\r\n9. Graph the line with slope \\(\\frac{1}{2}\\) containing the point \\(\\left(-3,-4\\right)\\).<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Graph the line for each of the following equations<\/h2>\r\n\r\n\r\n\r\n\r\n\r\n
    10. \\(y=\\frac{5}{3}x-1\\)<\/td>\r\n11. \\(y=-x\\)<\/td>\r\n<\/tr>\r\n
    12. \\(x-y=2\\)<\/td>\r\n13. \\(4x+2y=-8\\)<\/td>\r\n<\/tr>\r\n
    14. \\(y=2\\)<\/td>\r\n15. \\(x=-3\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Find the equation of each line. Write the equation in slope\u2013intercept form.<\/h2>\r\n\r\n\r\n\r\n\r\n\r\n
    16. slope \\(-\\frac{3}{4}\\) and y<\/em>-intercept \\(\\left(0,-2\\right)\\)<\/td>\r\n17. \\(m=2\\), point \\(\\left(-3,-1\\right)\\)<\/td>\r\n<\/tr>\r\n
    18. containing \\(\\left(10,1\\right)\\) and \\(\\left(6,-1\\right)\\)<\/td>\r\n19. parallel to the line \\(y=-\\frac{2}{3}x-1\\), containing the point \\(\\left(-3,8\\right)\\)<\/td>\r\n<\/tr>\r\n
    20. perpendicular to the line \\(y=\\frac{5}{4}x+2\\), containing the point \\(\\left(-10,3\\right)\\)<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Practice Test Answers<\/h1>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    1. \"\"<\/td>\r\n2. a) yes\u2003b) yes\u2003c) no<\/td>\r\n<\/tr>\r\n
    3. Answer may vary<\/td>\r\n4. \\(\\left(3,0\\right),\\left(0,-4\\right)\\)<\/td>\r\n<\/tr>\r\n
    5. m = \\(\\frac{-3}{5}\\)<\/td>\r\n6. undefined<\/td>\r\n<\/tr>\r\n
    7. m = 0<\/td>\r\n8. \\(1\\)<\/td>\r\n<\/tr>\r\n
    9. y = \\(\\frac{1}{2}\\)x - \\(\\frac{5}{2}\\)<\/td>\r\n10. \"The<\/span><\/td>\r\n<\/tr>\r\n
    11. \"\"<\/td>\r\n12.\"The<\/span><\/td>\r\n<\/tr>\r\n
    13. \"\"<\/td>\r\n14.\"The<\/td>\r\n<\/tr>\r\n
    15. \"\"<\/td>\r\n16. \\(y=-\\frac{3}{4}x-2\\)<\/td>\r\n<\/tr>\r\n
    17.\\(y = 2x + 5\\)<\/td>\r\n18. \\(y=\\frac{1}{2}x-4\\)<\/td>\r\n<\/tr>\r\n
    19. \\(y = -\\frac{2}{3}x+6\\)<\/td>\r\n20. \\(y=-\\frac{4}{5}x-5\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Attributions<\/h1>\r\nThis chapter has been adapted from \u201cReview Exercises\u201d and \u201cPractice Test\u201d in Chapter 4 of Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"

    Review Exercises<\/h1>\n

    Plot Points in a Rectangular Coordinate System<\/h2>\n

    In the following exercises, plot each point in a rectangular coordinate system.<\/p>\n\n\n\n\n
    1.
    \na) \"\left(4,3\right)\"
    \nb) \"\left(-4,3\right)\"
    \nc) \"\left(-4,-3\right)\"
    \nd) \"\left(4,-3\right)\"<\/td>\n    		2.
    \na) \"\left(-1,-5\right)\"
    \nb) \"\left(-3,4\right)\"
    \nc) \"\left(2,-3\right)\"
    \nd) \"\left(1,\frac{5}{2}\right)\"<\/td>\n<\/tr>\n
    3.
    \na) \"\left(2,\frac{3}{2}\right)\"
    \nb) \"\left(3,\frac{4}{3}\right)\"
    \nc) \"\left(\frac{1}{3},-4\right)\"
    \nd) \"\left(\frac{1}{2},-5\right)\"<\/td>\n    		4.
    \na) \"\left(-2,0\right)\"
    \nb) \"\left(0,-4\right)\"
    \nc) \"\left(0,5\right)\"
    \nd) \"\left(3,0\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Identify Points on a Graph<\/h2>\n

    In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.<\/p>\n\n\n\n
    5.\"The<\/span><\/span><\/td>\n6.\"The<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Verify Solutions to an Equation in Two Variables<\/h2>\n

    In the following exercises, which ordered pairs are solutions to the given equations?<\/p>\n\n\n\n
    \n

    7. \"y=6x-2\"<\/p>\n

    a) \"\left(1,4\right)\"
    \nb) \"\left(\frac{1}{3},0\right)\"
    \nc) \"\left(6,-2\right)\"<\/p>\n<\/td>\n

    		\n

    8. \"5x+y=10\"<\/p>\n

    a) \"\left(5,1\right)\"
    \nb) \"\left(2,0\right)\"
    \nc) \"\left(4,-10\right)\"<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Complete a Table of Solutions to a Linear Equation in Two Variables<\/h2>\n

    In the following exercises, complete the table to find solutions to each linear equation.<\/p>\n\n\n\n
    \n

    9. \"y=-\frac{1}{2}x+3\"<\/p>\n\n\n\n\n\n\n
    \"x\"<\/strong><\/td>\n\"y\"<\/strong><\/td>\n\"\left(x,y\right)\"<\/strong><\/td>\n<\/tr>\n
    0<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
    4<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
    \"-2\"<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n\n

    10. \"y=4x-1\"<\/p>\n\n\n\n\n\n\n\n
    \"x\"<\/strong><\/td>\n\"y\"<\/strong><\/td>\n\"\left(x,y\right)\"<\/strong><\/td>\n<\/tr>\n
    \"0\"<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
    \"1\"<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
    \"-2\"<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n
    \n

    11. \"3x+2y=6\"<\/p>\n\n\n\n\n\n\n
    \"x\"<\/td>\n\"y\"<\/td>\n\"\left(x,y\right)\"<\/td>\n<\/tr>\n
    0<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
    <\/td>\n0<\/td>\n<\/td>\n<\/tr>\n
    \"-2\"<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n\n

    12. \"x+2y=5\"<\/p>\n\n\n\n\n\n\n
    \"x\"<\/strong><\/td>\n\"y\"<\/strong><\/td>\n\"\left(x,y\right)\"<\/strong><\/td>\n<\/tr>\n
    <\/td>\n0<\/td>\n<\/td>\n<\/tr>\n
    1<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
    \"-1\"<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Find Solutions to a Linear Equation in Two Variables<\/h2>\n

    In the following exercises, find three solutions to each linear equation.<\/p>\n\n\n\n\n
    13. \"x+y=-4\"<\/td>\n14. \"x+y=3\"<\/td>\n<\/tr>\n
    15. \"y=\text{-}x-1\"<\/td>\n16. \"y=3x+1\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Recognize the Relation Between the Solutions of an Equation and its Graph<\/h2>\n

    In the following exercises, for each ordered pair, decide:<\/p>\n

    a) Is the ordered pair a solution to the equation?<\/p>\n

    b) Is the point on the line?<\/p>\n\n\n\n
    17.<\/p>\n

    \"y=\frac{2}{3}x-1\"<\/p>\n

    \"\left(0,-1\right)\" (3, 1)<\/p>\n

    \"\left(-3,-3\right)\" (6, 4)<\/p>\n

    \"The<\/span><\/td>\n

    		18.<\/p>\n

    \"y=\text{-}x+4\"<\/p>\n

    \"\left(0,4\right)\"\"\left(-1,3\right)\"<\/p>\n

    \"\left(2,2\right)\"\"\left(-2,6\right)\"<\/p>\n

    \"The<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Graph a Linear Equation by Plotting Points<\/h2>\n

    In the following exercises, graph by plotting points.<\/p>\n\n\n\n\n\n
    19. \"y=-3x\"<\/td>\n20. \"y=4x-3\"<\/td>\n<\/tr>\n
    21. \"x-y=6\"<\/td>\n22. \"y=\frac{1}{2}x+3\"<\/td>\n<\/tr>\n
    23. \"3x-2y=6\"<\/td>\n24. \"2x+y=7\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Graph Vertical and Horizontal lines<\/h2>\n

    In the following exercises, graph each equation.<\/p>\n\n\n\n
    25. \"x=3\"<\/td>\n26. \"y=-2\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    In the following exercises, graph each pair of equations in the same rectangular coordinate system.<\/p>\n\n\n\n
    27. \"y=\frac{4}{3}x\" and \"y=\frac{4}{3}\"<\/td>\n28. \"y=-2x\" and \"y=-2\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Identify the x<\/em>– and y<\/em>-Intercepts on a Graph<\/h2>\n

    In the following exercises, find the x<\/em>– and y<\/em>-intercepts.<\/p>\n\n\n\n
    29.\"The<\/span><\/span><\/td>\n30. \"The<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Find the x<\/em>– and y<\/em>-Intercepts from an Equation of a Line<\/h2>\n

    In the following exercises, find the intercepts of each equation.<\/p>\n\n\n\n\n\n
    31. \"x-y=-1\"<\/td>\n32. \"x+y=5\"<\/td>\n<\/tr>\n
    33. \"2x+3y=12\"<\/td>\n34. \"x+2y=6\"<\/td>\n<\/tr>\n
    35. \"y=3x\"<\/td>\n36. \"y=\frac{3}{4}x-12\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Graph a Line Using the Intercepts<\/h2>\n

    In the following exercises, graph using the intercepts.<\/p>\n\n\n\n\n\n
    37. \"-x+3y=3\"<\/td>\n38. \"x+y=-2\"<\/td>\n<\/tr>\n
    39. \"x-y=4\"<\/td>\n40. \"2x-y=5\"<\/td>\n<\/tr>\n
    41. \"2x-4y=8\"<\/td>\n42. \"y=2x\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Use Geoboards to Model Slope<\/h2>\n

    In the following exercises, find the slope modeled on each geoboard.<\/p>\n\n\n\n\n
    43. \"The<\/span><\/span><\/td>\n44. \"The<\/span><\/span><\/td>\n<\/tr>\n
    45. \"The<\/span><\/span><\/td>\n46. \"The<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    In the following exercises, model each slope. Draw a picture to show your results.<\/p>\n\n\n\n\n
    47. \"\frac{3}{2}\"<\/td>\n48. \"\frac{1}{3}\"<\/td>\n<\/tr>\n
    49. \"-\frac{1}{2}\"<\/td>\n50. \"-\frac{2}{3}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    In the following exercises, find the slope of each line shown. Use \"m=\frac{\text{rise}}{\text{run}}\" to find the slope of a line from its graph.<\/p>\n\n\n\n\n
    51. \"The<\/span><\/span><\/td>\n52. \"The<\/span><\/span><\/td>\n<\/tr>\n
    53. \"The<\/span><\/span><\/td>\n54. \"\"<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Find the Slope of Horizontal and Vertical Lines<\/h2>\n

    In the following exercises, find the slope of each line.<\/p>\n\n\n\n\n
    55. \"x=5\"<\/td>\n56. \"y=2\"<\/td>\n<\/tr>\n
    57. \"y=-1\"<\/td>\n58. \"x=-3\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Use the Slope Formula to find the Slope of a Line between Two Points<\/h2>\n

    In the following exercises, use the slope formula to find the slope of the line between each pair of points.<\/p>\n\n\n\n\n
    59. \"\left(3,5\right),\left(4,-1\right)\"<\/td>\n60. \"\left(-1,-1\right),\left(0,5\right)\"<\/td>\n<\/tr>\n
    61. \"\left(2,1\right),\left(4,6\right)\"<\/td>\n62. \"\left(-5,-2\right),\left(3,2\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Graph a Line Given a Point and the Slope<\/h2>\n

    In the following exercises, graph each line with the given point and slope.<\/p>\n\n\n\n\n
    63. \"\left(-3,4\right)\"; \"m=-\frac{1}{3}\"<\/td>\n64. \"\left(2,-2\right)\"; \"m=\frac{5}{2}\"<\/td>\n<\/tr>\n
    65. y<\/em>-intercept 1; \"m=-\frac{3}{4}\"<\/td>\n66. x<\/em>-intercept \"-4\"; \"m=3\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Solve Slope Applications<\/h2>\n

    In the following exercises, solve these slope applications.<\/p>\n\n\n\n
    67. A mountain road rises 50 feet for a 500-foot run. What is its slope? <\/span><\/td>\n68. The roof pictured below has a rise of 10 feet and a run of 15 feet. What is its slope?
    \n\"The<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Recognize the Relation Between the Graph and the Slope\u2013Intercept Form of an Equation of a Line<\/h2>\n

    In the following exercises, use the graph to find the slope and y<\/em>-intercept of each line. Compare the values to the equation \"y=mx+b\".<\/p>\n\n\n\n
    69.<\/span><\/p>\n

    \"The<\/span><\/p>\n

    \"y=-\frac{2}{3}x+4\"<\/p>\n<\/td>\n

    		70.<\/span><\/p>\n

    \"The<\/span><\/p>\n

    \"y=4x-1\"<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Identify the Slope and y-Intercept from an Equation of a Line<\/h2>\n

    In the following exercises, identify the slope and y<\/em>-intercept of each line.<\/p>\n\n\n\n\n
    71. \"y=\frac{5}{3}x-6\"<\/td>\n72. \"y=-4x+9\"<\/td>\n<\/tr>\n
    73. \"4x-5y=8\"<\/td>\n74. \"5x+y=10\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Graph a Line Using Its Slope and Intercept<\/h2>\n

    In the following exercises, graph the line of each equation using its slope and y<\/em>-intercept.<\/p>\n\n\n\n\n
    75. \"y=\text{-}x-1\"<\/td>\n76. \"y=2x+3\"<\/td>\n<\/tr>\n
    77. \"4x-3y=12\"<\/td>\n78. \"y=-\frac{2}{5}x+3\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    In the following exercises, determine the most convenient method to graph each line.<\/p>\n\n\n\n\n\n
    79. \"y=-3\"<\/td>\n80. \"x=5\"<\/td>\n<\/tr>\n
    81. \"x-y=2\"<\/td>\n82. \"2x+y=5\"<\/td>\n<\/tr>\n
    83. \"y=\frac{3}{4}x-1\"<\/td>\n84. \"y=x+2\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Graph and Interpret Applications of Slope\u2013Intercept<\/h2>\n\n\n\n
    \n

    85. Marjorie teaches piano. The equation \"P=35h-250\" models the relation between her weekly profit, P<\/em>, in dollars and the number of student lessons, s<\/em>, that she teaches.<\/p>\n

      \n
    1. Find Marjorie\u2019s profit for a week when she teaches no student lessons.<\/li>\n
    2. Find the profit for a week when she teaches 20 student lessons.<\/li>\n
    3. Interpret the slope and P<\/em>\u2013intercept of the equation.<\/li>\n
    4. Graph the equation.<\/li>\n<\/ol>\n<\/td>\n
    		\n

    86. Katherine is a private chef. The equation \"C=6.5m+42\" models the relation between her weekly cost, C<\/em>, in dollars and the number of meals, m<\/em>, that she serves.<\/p>\n

      \n
    1. Find Katherine\u2019s cost for a week when she serves no meals.<\/li>\n
    2. Find the cost for a week when she serves 14 meals.<\/li>\n
    3. Interpret the slope and C<\/em>-intercept of the equation.<\/li>\n
    4. Graph the equation.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Use Slopes to Identify Parallel Lines<\/h2>\n

      In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.<\/p>\n\n\n\n
      87. \"2x-y=8;\phantom{\rule{0.2em}{0ex}}x-2y=4\"<\/td>\n88. \"4x-3y=-1;\phantom{\rule{0.2em}{0ex}}y=\frac{4}{3}x-3\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Use Slopes to Identify Perpendicular Lines<\/h2>\n

      In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.<\/p>\n\n\n\n
      89. \"3x-2y=5;2x+3y=6\"<\/td>\n90. \"y=5x-1;10x+2y=0\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Find an Equation of the Line Given the Slope and y<\/em>-Intercept<\/h2>\n

      In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope\u2013intercept form.<\/p>\n\n\n\n\n
      91. slope \"-5\" and \"y\text{-intercept}\" \"\left(0,-3\right)\"<\/td>\n92. slope \"\frac{1}{3}\" and \"y\text{-intercept}\" \"\left(0,-6\right)\"<\/td>\n<\/tr>\n
      93. slope \"-2\" and \"y\text{-intercept}\" \"\left(0,0\right)\"<\/td>\n94. slope \"0\" and \"y\text{-intercept}\" \"\left(0,4\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      In the following exercises, find the equation of the line shown in each graph. Write the equation in slope\u2013intercept form.<\/p>\n\n\n\n\n
      95. \"The<\/span><\/span><\/td>\n96. \"The<\/span><\/span><\/td>\n<\/tr>\n
      97. \"The<\/span><\/span><\/td>\n98. \"The<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Find an Equation of the Line Given the Slope and a Point<\/h2>\n

      In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope\u2013intercept form.<\/p>\n\n\n\n\n
      99. \"m=\frac{3}{5}\", point \"\left(10,6\right)\"<\/td>\n100. \"m=-\frac{1}{4}\", point \"\left(-8,3\right)\"<\/td>\n<\/tr>\n
      101. \"m=-2\", point \"\left(-1,-3\right)\"<\/td>\n102. Horizontal line containing \"\left(-2,7\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Find an Equation of the Line Given Two Points<\/h2>\n

      In the following exercises, find the equation of a line containing the given points. Write the equation in slope\u2013intercept form.<\/p>\n\n\n\n\n
      103. \"\left(7,1\right)\" and \"\left(5,0\right)\"<\/td>\n104. \"\left(2,10\right)\" and \"\left(-2,-2\right)\"<\/td>\n<\/tr>\n
      105. \"\left(5,2\right)\" and \"\left(-1,2\right)\"<\/td>\n106. \"\left(3,8\right)\" and \"\left(3,-4\right)\".<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Find an Equation of a Line Parallel to a Given Line<\/h2>\n

      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\u2013intercept form.<\/p>\n\n\n\n\n
      107. line \"2x+5y=-10\", point \"\left(10,4\right)\"<\/td>\n108. line \"y=-3x+6\", point \"\left(1,-5\right)\"<\/td>\n<\/tr>\n
      109. line \"y=-5\", point \"\left(-4,3\right)\"<\/td>\n110. line \"x=4\", point \"\left(-2,-1\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Find an Equation of a Line Perpendicular to a Given Line<\/h2>\n

      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\u2013intercept form.<\/p>\n\n\n\n\n
      111. line \"2x-3y=9\", point \"\left(-4,0\right)\"<\/td>\n112. line \"y=-\frac{4}{5}x+2\", point \"\left(8,9\right)\"<\/td>\n<\/tr>\n
      113. line \"x=-5\" point \"\left(2,1\right)\"<\/td>\n114. line \"y=3\", point \"\left(-1,-3\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Review Answers<\/h1>\n\n\n\n\n\n
      1. \"The<\/span><\/td>\n3. \"The<\/span><\/td>\n<\/tr>\n
      5. a) \"\left(2,0\right)\"\u2003b) \"\left(0,-5\right)\"\u2003c) \"\left(-4.0\right)\"\u2003d) \"\left(0,3\right)\"<\/td>\n7. a, b<\/td>\n<\/tr>\n
      9.<\/p>\n\n\n\n\n\n\n
      \"x\"<\/strong><\/td>\n\"y\"<\/strong><\/td>\n\"\left(x,y\right)\"<\/strong><\/td>\n<\/tr>\n
      0<\/td>\n3<\/td>\n\"\left(0,3\right)\"<\/td>\n<\/tr>\n
      4<\/td>\n1<\/td>\n(4, 1)<\/td>\n<\/tr>\n
      \"-2\"<\/td>\n4<\/td>\n\"\left(-2,4\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n11.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
      \"x\"<\/td>\n\"y\"<\/td>\n\"\left(x,y\right)\"<\/td>\n<\/tr>\n
      0<\/td>\n\"-3\"<\/td>\n\"\left(0,-3\right)\"<\/td>\n<\/tr>\n
      2<\/td>\n0<\/td>\n\"\left(2,0\right)\"<\/td>\n<\/tr>\n
      \"-2\"<\/td>\n\"-6\"<\/td>\n\"\left(-2,-6\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n
      13. Answers will vary.<\/td>\n15. Answers will vary.<\/td>\n<\/tr>\n
      17. a) yes; yes\u2003b) yes; no<\/td>\n19.\"The<\/span><\/td>\n<\/tr>\n
      21. \"The<\/span><\/td>\n23. \"The<\/span><\/td>\n<\/tr>\n
      25. \"The<\/span><\/td>\n27. \"The<\/span><\/td>\n<\/tr>\n
      29. \"\left(3,0\right),\left(0,3\right)\"<\/td>\n31. \"\left(-1,0\right),\left(0,1\right)\"<\/td>\n<\/tr>\n
      33. \"\left(6,0\right),\left(0,4\right)\"<\/td>\n35. \"\left(0,0\right)\"<\/td>\n<\/tr>\n
      37. \"Graph<\/a><\/td>\n39. \"Graph<\/a><\/td>\n<\/tr>\n
      41. \"graph<\/a><\/td>\n43. \"\frac{4}{3}\"<\/td>\n<\/tr>\n
      45. \"-\frac{2}{3}\"<\/td>\n47. \"The<\/span><\/td>\n<\/tr>\n
      49. \"The<\/span><\/td>\n51. 1<\/td>\n<\/tr>\n
      53. \"-\frac{1}{2}\"<\/td>\n55. undefined<\/td>\n<\/tr>\n
      57. 0<\/td>\n59. \"-6\"<\/td>\n<\/tr>\n
      61. \"\frac{5}{2}\"<\/td>\n63. \"The<\/span><\/td>\n<\/tr>\n
      65. \"The<\/span><\/td>\n67. \"\frac{1}{10}\"<\/td>\n<\/tr>\n
      69. slope \"m=-\frac{2}{3}\" and y<\/em>-intercept \"\left(0,4\right)\"<\/td>\n71. \"\frac{5}{3};\left(0,-6\right)\"<\/td>\n<\/tr>\n
      73. \"\frac{4}{5};\left(0,-\frac{8}{5}\right)\"<\/td>\n75. \"The<\/span><\/td>\n<\/tr>\n
      77. \"The<\/span><\/td>\n79. horizontal line<\/td>\n<\/tr>\n
      81. intercepts<\/td>\n83. plotting points<\/td>\n<\/tr>\n
      85. a) \u2212250\u2003b) 450\u2003c) The slope, 35, means that Marjorie\u2019s weekly profit, P<\/em>, increases by $35 for each additional student lesson she teaches. The P<\/em>\u2013intercept means that when the number of lessons is 0, Marjorie loses $250.\u2003d)
      \n\"The<\/span><\/td>\n      		87. not parallel<\/td>\n<\/tr>\n
      89. perpendicular<\/td>\n91. \"y=-5x-3\"<\/td>\n<\/tr>\n
      93. \"y=-2x\"<\/td>\n95. \"y=-3x+5\"<\/td>\n<\/tr>\n
      97. \"y=-4\"<\/td>\n99. \"y=\frac{3}{5}x\"<\/td>\n<\/tr>\n
      101. \"y=-2x-5\"<\/td>\n103. \"y=\frac{1}{2}x-\frac{5}{2}\"<\/td>\n<\/tr>\n
      105. \"y=2\"<\/td>\n107. \"y=-\frac{2}{5}x+8\"<\/td>\n<\/tr>\n
      109. \"y=3\"<\/td>\n111. \"y=-\frac{3}{2}x-6\"<\/td>\n<\/tr>\n
      113. \"y=1\"<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Practice Test<\/h1>\n\n\n\n\n
      1. Plot each point in a rectangular coordinate system.<\/p>\n

      a) \"\left(2,5\right)\"
      \nb) \"\left(-1,-3\right)\"
      \nc) \"\left(0,2\right)\"
      \nd) \"\left(-4,\frac{3}{2}\right)\"
      \ne) \"\left(5,0\right)\"<\/p>\n<\/td>\n

      		\n

      2. Which of the given ordered pairs are solutions to the equation \"3x-y=6\"?<\/p>\n

      a) \"\left(3,3\right)\"
      \nb) \"\left(2,0\right)\"
      \nc) \"\left(4,-6\right)\"<\/p>\n<\/td>\n<\/tr>\n

      3. Find three solutions to the linear equation \"y=-2x-4\".<\/td>\n4. Find the x<\/em>– and y<\/em>-intercepts of the equation \"4x-3y=12\".<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Find the slope of each line shown.<\/h2>\n\n\n\n\n
      5. \"The<\/span><\/td>\n6. \"The<\/span><\/td>\n<\/tr>\n
      7. \"The<\/span><\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
      8. Find the slope of the line between the points \"\left(5,2\right)\" and \"\left(-1,-4\right)\".<\/td>\n9. Graph the line with slope \"\frac{1}{2}\" containing the point \"\left(-3,-4\right)\".<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Graph the line for each of the following equations<\/h2>\n\n\n\n\n\n
      10. \"y=\frac{5}{3}x-1\"<\/td>\n11. \"y=-x\"<\/td>\n<\/tr>\n
      12. \"x-y=2\"<\/td>\n13. \"4x+2y=-8\"<\/td>\n<\/tr>\n
      14. \"y=2\"<\/td>\n15. \"x=-3\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Find the equation of each line. Write the equation in slope\u2013intercept form.<\/h2>\n\n\n\n\n\n
      16. slope \"-\frac{3}{4}\" and y<\/em>-intercept \"\left(0,-2\right)\"<\/td>\n17. \"m=2\", point \"\left(-3,-1\right)\"<\/td>\n<\/tr>\n
      18. containing \"\left(10,1\right)\" and \"\left(6,-1\right)\"<\/td>\n19. parallel to the line \"y=-\frac{2}{3}x-1\", containing the point \"\left(-3,8\right)\"<\/td>\n<\/tr>\n
      20. perpendicular to the line \"y=\frac{5}{4}x+2\", containing the point \"\left(-10,3\right)\"<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Practice Test Answers<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n
      1. \"\"<\/td>\n2. a) yes\u2003b) yes\u2003c) no<\/td>\n<\/tr>\n
      3. Answer may vary<\/td>\n4. \"\left(3,0\right),\left(0,-4\right)\"<\/td>\n<\/tr>\n
      5. m = \"\frac{-3}{5}\"<\/td>\n6. undefined<\/td>\n<\/tr>\n
      7. m = 0<\/td>\n8. \"1\"<\/td>\n<\/tr>\n
      9. y = \"\frac{1}{2}\"x – \"\frac{5}{2}\"<\/td>\n10. \"The<\/span><\/td>\n<\/tr>\n
      11. \"\"<\/td>\n12.\"The<\/span><\/td>\n<\/tr>\n
      13. \"\"<\/td>\n14.\"The<\/td>\n<\/tr>\n
      15. \"\"<\/td>\n16. \"y=-\frac{3}{4}x-2\"<\/td>\n<\/tr>\n
      17.\"y = 2x + 5\"<\/td>\n18. \"y=\frac{1}{2}x-4\"<\/td>\n<\/tr>\n
      19. \"y = -\frac{2}{3}x+6\"<\/td>\n20. \"y=-\frac{4}{5}x-5\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Attributions<\/h1>\n

      This chapter has been adapted from \u201cReview Exercises\u201d and \u201cPractice Test\u201d in Chapter 4 of Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":999,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-1525","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":1001,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1525","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":11,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1525\/revisions"}],"predecessor-version":[{"id":2131,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1525\/revisions\/2131"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/parts\/1001"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1525\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/media?parent=1525"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapter-type?post=1525"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/contributor?post=1525"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/license?post=1525"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}