{"id":1331,"date":"2019-06-14T18:27:10","date_gmt":"2019-06-14T22:27:10","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1331"},"modified":"2019-11-04T12:46:11","modified_gmt":"2019-11-04T17:46:11","slug":"answer-key-3-5","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-3-5\/","title":{"raw":"Answer Key 3.5","rendered":"Answer Key 3.5"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&3&=&\\dfrac{2}{3}(x&-&2) \\\\ \\\\\r\ny&-&3&=&\\dfrac{2}{3}x&-&\\dfrac{4}{3} \\\\ \\\\\r\n&+&3&&&+&3 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{2}{3}x&+&\\dfrac{5}{3}\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&2&=&4(x&-&1) \\\\\r\ny&-&2&=&4x&-&4 \\\\\r\n&+&2&&&+&2 \\\\\r\n\\midrule\r\n&&y&=&4x&-&2\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&2&=&\\dfrac{1}{2}(x&-&2) \\\\ \\\\\r\ny&-&2&=&\\dfrac{1}{2}x&-&1 \\\\\r\n&+&2&&&+&2 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{1}{2}x&+&1\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&1&=&-\\dfrac{1}{2}(x&-&2) \\\\ \\\\\r\ny&-&1&=&-\\dfrac{1}{2}x&+&1 \\\\\r\n&+&1&&&+&1 \\\\\r\n\\midrule\r\n&&y&=&-\\dfrac{1}{2}x&+&2\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-5&=&9(x&-&-1) \\\\\r\ny&+&5&=&9x&+&9 \\\\\r\n&-&5&&&-&5 \\\\\r\n\\midrule\r\n&&y&=&9x&+&4\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-2&=&-2(x&-&2) \\\\\r\ny&+&2&=&-2x&+&4 \\\\\r\n&-&2&&&-&2 \\\\\r\n\\midrule\r\n&&y&=&-2x&+&2\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&1&=&\\dfrac{3}{4}(x&-&-4) \\\\ \\\\\r\ny&-&1&=&\\dfrac{3}{4}x&+&3 \\\\\r\n&+&1&&&+&1 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{3}{4}x&+&4\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-3&=&-2(x&-&4) \\\\\r\ny&+&3&=&-2x&+&8 \\\\\r\n&-&3&&&-&3 \\\\\r\n\\midrule\r\n&&y&=&-2x&+&5\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-2&=&-3(x&-&0) \\\\\r\ny&+&2&=&-3x&& \\\\\r\n&-&2&&&-&2 \\\\\r\n\\midrule\r\n&&y&=&-3x&-&2 \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&1&=&4(x&-&-1) \\\\\r\ny&-&1&=&4x&+&4 \\\\\r\n&+&1&&&+&1 \\\\\r\n\\midrule\r\n&&y&=&4x&+&5\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-5&=&-\\dfrac{1}{4}(x&-&0) \\\\ \\\\\r\ny&+&5&=&-\\dfrac{1}{4}x&& \\\\\r\n&-&5&&&-&5 \\\\\r\n\\midrule\r\n&&y&=&-\\dfrac{1}{4}x&-&5\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&2&=&-\\dfrac{5}{4}(x&-&0) \\\\ \\\\\r\ny&-&2&=&-\\dfrac{5}{4}x&& \\\\\r\n&+&2&&&+&2 \\\\\r\n\\midrule\r\n&&y&=&-\\dfrac{5}{4}x&+&2\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&& \\\\\r\ny&-&-5&=&2(x&-&-1)&& \\\\\r\ny&+&5&=&2x&+&2&& \\\\\r\n-y&-&5&&-y&-&5&& \\\\\r\n\\midrule\r\n&&0&=&2x&-&y&-&3\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\r\ny&-&-2&=&-2(x&-&2)&&& \\\\\r\ny&+&2&=&-2x&+&4&&& \\\\\r\n-y&-&2&&-y&-&2&&& \\\\\r\n\\midrule\r\n&&(0&=&-2x&-&y&+&2)&(-1) \\\\\r\n&&0&=&2x&+&y&-&2&\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\r\ny&-&-1&=&-\\dfrac{3}{5}(x&-&5)&&& \\\\ \\\\\r\ny&+&1&=&-\\dfrac{3}{5}x&+&3&&& \\\\ \\\\\r\n-y&-&1&&-y&-&1&&& \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{3}{5}x&-&y&+&2)&(-5) \\\\ \\\\\r\n&&0&=&3x&+&5y&-&10&\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-2&=&-\\dfrac{2}{3}(x&-&-2) \\\\ \\\\\r\ny&+&2&=&-\\dfrac{2}{3}x&-&\\dfrac{4}{3} \\\\ \\\\\r\n-y&-&2&&-y&-&2 \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{2}{3}x&-&y&-&\\dfrac{10}{3})&(-3) \\\\ \\\\\r\n&&0&=&2x&+&3y&+&10&\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&1&=&\\dfrac{1}{2}(x&-&-4) \\\\ \\\\\r\ny&-&1&=&\\dfrac{1}{2}x&+&2 \\\\ \\\\\r\n-y&+&1&&-y&+&1 \\\\\r\n\\midrule\r\n&&(0&=&\\dfrac{1}{2}x&-&y&+&3)&(2) \\\\ \\\\\r\n&&0&=&x&-&2y&+&6&\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-3&=&-\\dfrac{7}{4}(x&-&4) \\\\ \\\\\r\ny&+&3&=&-\\dfrac{7}{4}x&+&7 \\\\ \\\\\r\n-y&-&3&&-y&-&3 \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{7}{4}x&-&y&+&4)&(-4) \\\\ \\\\\r\n&&0&=&7x&+&4y&-&16&\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-2&=&-\\dfrac{3}{2}(x&-&4) \\\\ \\\\\r\ny&+&2&=&-\\dfrac{3}{2}x&+&6 \\\\ \\\\\r\n-y&-&2&&-y&-&2 \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{3}{2}x&-&y&+&4)&(-2) \\\\ \\\\\r\n&&0&=&3x&+&2y&-&8&\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&0&=&-\\dfrac{5}{2}(x&-&-2) \\\\ \\\\\r\n&&y&=&-\\dfrac{5}{2}x&-&5 \\\\ \\\\\r\n&&-y&&-y&& \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{5}{2}x&-&y&+&5)&(-2) \\\\ \\\\\r\n&&0&=&5x&+&2y&+&10&\r\n\\end{array}\\)<\/li>\r\n \t
  21. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-3&=&-\\dfrac{2}{5}(x&-&-5) \\\\ \\\\\r\ny&+&3&=&-\\dfrac{2}{5}x&-&2 \\\\ \\\\\r\n-y&-&3&&-y&-&3 \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{2}{5}x&-&y&-&5)&(-5) \\\\ \\\\\r\n&&0&=&2x&+&5y&+&25&\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&3&=&\\dfrac{7}{3}(x&-&3) \\\\ \\\\\r\ny&-&3&=&\\dfrac{7}{3}x&-&7 \\\\ \\\\\r\n-y&+&3&&-y&+&3 \\\\\r\n\\midrule\r\n&&(0&=&\\dfrac{7}{3}x&-&y&-&4)&(3) \\\\ \\\\\r\n&&0&=&7x&-&3y&-&12&\r\n\\end{array}\\)<\/li>\r\n \t
  23. \\(\\begin{array}{rrrrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&& \\\\\r\ny&-&-2&=&1(x&-&2)&& \\\\\r\ny&+&2&=&x&-&2&& \\\\\r\n-y&-&2&&-y&-&2&& \\\\\r\n\\midrule\r\n&&0&=&x&-&y&-&4\r\n\\end{array}\\)<\/li>\r\n \t
  24. \\(\\begin{array}{rrrrlrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&4&=&-\\dfrac{1}{3}(x&-&-3) \\\\ \\\\\r\ny&-&4&=&-\\dfrac{1}{3}x&-&1 \\\\ \\\\\r\n-y&+&4&&-y&+&4 \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{1}{3}x&-&y&+&3)&(-3) \\\\ \\\\\r\n&&0&=&x&+&3y&-&9&\r\n\\end{array}\\)<\/li>\r\n \t
  25. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{1-3}{-3--4}\\Rightarrow \\dfrac{-2}{1}\\Rightarrow -2 \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&1&=&-2(x&-&-3) \\\\\r\ny&-&1&=&-2x&-&6 \\\\\r\n&+&1&&&+&1 \\\\\r\n\\midrule\r\n&&y&=&-2x&-&5\r\n\\end{array}\\)<\/li>\r\n \t
  26. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-3-3}{-3-1}\\Rightarrow \\dfrac{-6}{-4}\\Rightarrow \\dfrac{3}{2} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&3&=&\\dfrac{3}{2}(x&-&1) \\\\ \\\\\r\ny&-&3&=&\\dfrac{3}{2}x&-&\\dfrac{3}{2} \\\\ \\\\\r\n&+&3&&&+&3 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{3}{2}x&+&\\dfrac{3}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  27. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{0-1}{-3-5}\\Rightarrow \\dfrac{-1}{-8}\\Rightarrow \\dfrac{1}{8} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&0&=&\\dfrac{1}{8}(x&-&-3) \\\\ \\\\\r\n&&y&=&\\dfrac{1}{8}x&+&\\dfrac{3}{8}\r\n\\end{array}\\)<\/li>\r\n \t
  28. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4-5}{4--4}\\Rightarrow \\dfrac{-1}{8} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&4&=&-\\dfrac{1}{8}(x&-&4) \\\\ \\\\\r\ny&-&4&=&-\\dfrac{1}{8}x&+&\\dfrac{1}{2} \\\\ \\\\\r\n&+&4&&&+&4 \\\\\r\n\\midrule\r\n&&y&=&-\\dfrac{1}{8}x&+&\\dfrac{9}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  29. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4--2}{0--4}\\Rightarrow \\dfrac{6}{4}\\Rightarrow \\dfrac{3}{2} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&4&=&\\dfrac{3}{2}(x&-&0) \\\\ \\\\\r\ny&-&4&=&\\dfrac{3}{2}x&& \\\\\r\n&+&4&&&+&4 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{3}{2}x&+&4\r\n\\end{array}\\)<\/li>\r\n \t
  30. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4-1}{4--4}\\Rightarrow \\dfrac{3}{8} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&4&=&\\dfrac{3}{8}(x&-&4) \\\\ \\\\\r\ny&-&4&=&\\dfrac{3}{8}x&-&\\dfrac{3}{2} \\\\ \\\\\r\n&+&4&&&+&4 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{3}{8}x&+&\\dfrac{5}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  31. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{3-5}{-5-3}\\Rightarrow \\dfrac{-2}{-8}\\Rightarrow \\dfrac{1}{4} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&3&=&\\dfrac{1}{4}(x&-&-5) \\\\ \\\\\r\ny&-&3&=&\\dfrac{1}{4}x&-&\\dfrac{5}{4} \\\\ \\\\\r\n&+&3&&&+&3 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{1}{4}x&+&\\dfrac{17}{4}\r\n\\end{array}\\)<\/li>\r\n \t
  32. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{0--4}{-5--1}\\Rightarrow \\dfrac{4}{-4}\\Rightarrow -1 \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&0&=&-1(x&-&-5) \\\\\r\n&&y&=&-x&-&5\r\n\\end{array}\\)<\/li>\r\n \t
  33. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{5--3}{-4-3}\\Rightarrow \\dfrac{8}{-7}\\Rightarrow -\\dfrac{8}{7} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&5&=&-\\dfrac{8}{7}(x&-&-4) \\\\ \\\\\r\ny&-&5&=&-\\dfrac{8}{7}x&-&\\dfrac{32}{7} \\\\ \\\\\r\n-y&+&5&&-y&+&5 \\\\\r\n\\midrule\r\n&&\\left(0&=&-\\dfrac{8}{7}x&-&y&+&\\dfrac{3}{7}) &(-7) \\\\ \\\\\r\n&&0&=&8x&+&7y&-&3&\r\n\\end{array}\\)<\/li>\r\n \t
  34. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--5}{-5--1}\\Rightarrow \\dfrac{1}{-4}\\Rightarrow -\\dfrac{1}{4} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-5&=&-\\dfrac{1}{4}(x&-&-1) \\\\ \\\\\r\ny&+&5&=&-\\dfrac{1}{4}(x&+&1) \\\\ \\\\\r\ny&+&5&=&-\\dfrac{1}{4}x&-&\\dfrac{1}{4} \\\\ \\\\\r\n-y&-&5&&-y&-&5 \\\\\r\n\\midrule\r\n&&\\left(0&=&-\\dfrac{1}{4}x&-&y&-&\\dfrac{21}{4}) &(-4) \\\\ \\\\\r\n&&0&=&x&+&4y&+&21&\r\n\\end{array}\\)<\/li>\r\n \t
  35. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4--3}{-2-3}\\Rightarrow \\dfrac{7}{-5}\\Rightarrow -\\dfrac{7}{5} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&4&=&-\\dfrac{7}{5}(x&-&-2) \\\\ \\\\\r\ny&-&4&=&-\\dfrac{7}{5}x&-&\\dfrac{14}{5} \\\\ \\\\\r\n-y&+&4&&-y&+&4 \\\\\r\n\\midrule\r\n&&\\left(0&=&-\\dfrac{7}{5}x&-&y&+&\\dfrac{6}{5}) &(-5) \\\\ \\\\\r\n&&0&=&7x&+&5y&-&6&\r\n\\end{array}\\)<\/li>\r\n \t
  36. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--7}{-3--6}\\Rightarrow \\dfrac{3}{3}\\Rightarrow 1 \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrr}\r\ny&-&y_1&=&m(x&-&x_1)&& \\\\\r\ny&-&-4&=&1(x&-&-3)&& \\\\\r\ny&+&4&=&x&+&3&& \\\\\r\n-y&-&4&&-y&-&4&& \\\\\r\n\\midrule\r\n&&0&=&x&-&y&-&1\r\n\\end{array}\\)<\/li>\r\n \t
  37. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-2-1}{-1--5}\\Rightarrow \\dfrac{-3}{4} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-2&=&-\\dfrac{3}{4}(x&-&-1) \\\\ \\\\\r\ny&+&2&=&-\\dfrac{3}{4}x&-&\\dfrac{3}{4} \\\\ \\\\\r\n-y&-&2&&-y&-&2 \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{3}{4}x&-&y&-&\\dfrac{11}{4}) &(-4) \\\\ \\\\\r\n&&0&=&3x&+&4y&+&11&\r\n\\end{array}\\)<\/li>\r\n \t
  38. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-2--1}{5--5}\\Rightarrow \\dfrac{-1}{10} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-1&=&-\\dfrac{1}{10}(x&-&-5) \\\\ \\\\\r\ny&+&1&=&-\\dfrac{1}{10}x&-&\\dfrac{1}{2} \\\\ \\\\\r\n-y&-&1&&-y&-&1 \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{1}{10}x&-&y&-&\\dfrac{3}{2}) &(-10) \\\\ \\\\\r\n&&0&=&x&+&10y&+&15&\r\n\\end{array}\\)<\/li>\r\n \t
  39. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-3-5}{2--5}\\Rightarrow \\dfrac{-8}{7} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-3&=&-\\dfrac{8}{7}(x&-&2) \\\\ \\\\\r\ny&+&3&=&-\\dfrac{8}{7}x&+&\\dfrac{16}{7} \\\\ \\\\\r\n-y&-&3&&-y&-&3 \\\\\r\n\\midrule\r\n&&(0&=&-\\dfrac{8}{7}x&-&y&-&\\dfrac{5}{7}) &(-7) \\\\ \\\\\r\n&&0&=&8x&+&7y&+&5&\r\n\\end{array}\\)<\/li>\r\n \t
  40. \\(\\phantom{1}\\)\r\n\\(m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--1}{-5-1}\\Rightarrow \\dfrac{-3}{-6}\\Rightarrow \\dfrac{1}{2} \\\\ \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrrr}\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-1&=&\\dfrac{1}{2}(x&-&1) \\\\ \\\\\r\ny&+&1&=&\\dfrac{1}{2}x&-&\\dfrac{1}{2} \\\\ \\\\\r\n-y&-&1&&-y&-&1 \\\\\r\n\\midrule\r\n&&(0&=&\\dfrac{1}{2}x&-&y&-&\\dfrac{3}{2}) &(2) \\\\ \\\\\r\n&&0&=&x&-&2y&-&3&\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\begin{array}{rrrrlrr}<\/li>\n
    2. \"\begin{array}{rrrrlrr}<\/li>\n
    3. \"\begin{array}{rrrrlrr}<\/li>\n
    4. \"\begin{array}{rrrrlrr}<\/li>\n
    5. \"\begin{array}{rrrrlrr}<\/li>\n
    6. \"\begin{array}{rrrrlrr}<\/li>\n
    7. \"\begin{array}{rrrrlrr}<\/li>\n
    8. \"\begin{array}{rrrrlrr}<\/li>\n
    9. \"\begin{array}{rrrrlrr}<\/li>\n
    10. \"\begin{array}{rrrrlrr}<\/li>\n
    11. \"\begin{array}{rrrrlrr}<\/li>\n
    12. \"\begin{array}{rrrrlrr}<\/li>\n
    13. \"\begin{array}{rrrrlrrrr}<\/li>\n
    14. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    15. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    16. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    17. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    18. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    19. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    20. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    21. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    22. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    23. \"\begin{array}{rrrrlrrrr}<\/li>\n
    24. \"\begin{array}{rrrrlrrrrr}<\/li>\n
    25. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{1-3}{-3--4}\Rightarrow \dfrac{-2}{1}\Rightarrow -2 \\ \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    26. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{-3-3}{-3-1}\Rightarrow \dfrac{-6}{-4}\Rightarrow \dfrac{3}{2} \\ \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    27. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{0-1}{-3-5}\Rightarrow \dfrac{-1}{-8}\Rightarrow \dfrac{1}{8} \\ \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    28. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{4-5}{4--4}\Rightarrow \dfrac{-1}{8} \\ \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    29. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{4--2}{0--4}\Rightarrow \dfrac{6}{4}\Rightarrow \dfrac{3}{2} \\ \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    30. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{4-1}{4--4}\Rightarrow \dfrac{3}{8} \\ \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    31. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{3-5}{-5-3}\Rightarrow \dfrac{-2}{-8}\Rightarrow \dfrac{1}{4} \\ \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    32. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{0--4}{-5--1}\Rightarrow \dfrac{4}{-4}\Rightarrow -1 \\ \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    33. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{5--3}{-4-3}\Rightarrow \dfrac{8}{-7}\Rightarrow -\dfrac{8}{7} \\ \\\"
      \n\"\begin{array}{rrrrlrrrrr}<\/li>\n
    34. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{-4--5}{-5--1}\Rightarrow \dfrac{1}{-4}\Rightarrow -\dfrac{1}{4} \\ \\\"
      \n\"\begin{array}{rrrrlrrrrr}<\/li>\n
    35. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{4--3}{-2-3}\Rightarrow \dfrac{7}{-5}\Rightarrow -\dfrac{7}{5} \\ \\\"
      \n\"\begin{array}{rrrrlrrrrr}<\/li>\n
    36. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{-4--7}{-3--6}\Rightarrow \dfrac{3}{3}\Rightarrow 1 \\ \\\"
      \n\"\begin{array}{rrrrlrrrr}<\/li>\n
    37. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{-2-1}{-1--5}\Rightarrow \dfrac{-3}{4} \\ \\\"
      \n\"\begin{array}{rrrrlrrrrr}<\/li>\n
    38. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{-2--1}{5--5}\Rightarrow \dfrac{-1}{10} \\ \\\"
      \n\"\begin{array}{rrrrlrrrrr}<\/li>\n
    39. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{-3-5}{2--5}\Rightarrow \dfrac{-8}{7} \\ \\\"
      \n\"\begin{array}{rrrrlrrrrr}<\/li>\n
    40. \"\phantom{1}\"
      \n\"m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{-4--1}{-5-1}\Rightarrow \dfrac{-3}{-6}\Rightarrow \dfrac{1}{2} \\ \\\"
      \n\"\begin{array}{rrrrlrrrrr}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":22,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1331","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1331","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":9,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1331\/revisions"}],"predecessor-version":[{"id":2951,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1331\/revisions\/2951"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1331\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1331"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1331"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1331"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}