{"id":1650,"date":"2021-12-02T19:38:55","date_gmt":"2021-12-03T00:38:55","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-5\/"},"modified":"2022-11-02T10:37:06","modified_gmt":"2022-11-02T14:37:06","slug":"answer-key-3-5","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-5\/","title":{"raw":"Answer Key 3.5","rendered":"Answer Key 3.5"},"content":{"raw":"
    \n \t
  1. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&3&=&\\dfrac{2}{3}(x&-&2) \\\\ \\\\\ny&-&3&=&\\dfrac{2}{3}x&-&\\dfrac{4}{3} \\\\ \\\\\n&+&3&&&+&3 \\\\\n\\hline\n&&y&=&\\dfrac{2}{3}x&+&\\dfrac{5}{3}\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&2&=&4(x&-&1) \\\\\ny&-&2&=&4x&-&4 \\\\\n&+&2&&&+&2 \\\\\n\\hline\n&&y&=&4x&-&2\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&2&=&\\dfrac{1}{2}(x&-&2) \\\\ \\\\\ny&-&2&=&\\dfrac{1}{2}x&-&1 \\\\\n&+&2&&&+&2 \\\\\n\\hline\n&&y&=&\\dfrac{1}{2}x&+&1\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&1&=&-\\dfrac{1}{2}(x&-&2) \\\\ \\\\\ny&-&1&=&-\\dfrac{1}{2}x&+&1 \\\\\n&+&1&&&+&1 \\\\\n\\hline\n&&y&=&-\\dfrac{1}{2}x&+&2\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-5&=&9(x&-&-1) \\\\\ny&+&5&=&9x&+&9 \\\\\n&-&5&&&-&5 \\\\\n\\hline\n&&y&=&9x&+&4\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-2&=&-2(x&-&2) \\\\\ny&+&2&=&-2x&+&4 \\\\\n&-&2&&&-&2 \\\\\n\\hline\n&&y&=&-2x&+&2\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&1&=&\\dfrac{3}{4}(x&-&-4) \\\\ \\\\\ny&-&1&=&\\dfrac{3}{4}x&+&3 \\\\\n&+&1&&&+&1 \\\\\n\\hline\n&&y&=&\\dfrac{3}{4}x&+&4\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-3&=&-2(x&-&4) \\\\\ny&+&3&=&-2x&+&8 \\\\\n&-&3&&&-&3 \\\\\n\\hline\n&&y&=&-2x&+&5\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-2&=&-3(x&-&0) \\\\\ny&+&2&=&-3x&& \\\\\n&-&2&&&-&2 \\\\\n\\hline\n&&y&=&-3x&-&2 \\\\\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&1&=&4(x&-&-1) \\\\\ny&-&1&=&4x&+&4 \\\\\n&+&1&&&+&1 \\\\\n\\hline\n&&y&=&4x&+&5\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-5&=&-\\dfrac{1}{4}(x&-&0) \\\\ \\\\\ny&+&5&=&-\\dfrac{1}{4}x&& \\\\\n&-&5&&&-&5 \\\\\n\\hline\n&&y&=&-\\dfrac{1}{4}x&-&5\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&2&=&-\\dfrac{5}{4}(x&-&0) \\\\ \\\\\ny&-&2&=&-\\dfrac{5}{4}x&& \\\\\n&+&2&&&+&2 \\\\\n\\hline\n&&y&=&-\\dfrac{5}{4}x&+&2\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\begin{array}[t]{rrrrlrrrr}\\quad y&-&y_1&=&m(x&-&x_1)&&\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrr}\ny&-&y_1&=&m(x&-&x_1)&& \\\\\ny&-&-5&=&2(x&-&-1)&& \\\\\ny&+&5&=&2x&+&2&& \\\\\n-y&-&5&&-y&-&5&& \\\\\n\\hline\n&&0&=&2x&-&y&-&3\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)&&&\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\ny&-&-2&=&-2(x&-&2)&&& \\\\\ny&+&2&=&-2x&+&4&&& \\\\\n-y&-&2&&-y&-&2&&& \\\\\n\\hline\n&&(0&=&-2x&-&y&+&2)&(-1) \\\\\n&&0&=&2x&+&y&-&2&\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)&&&\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\ny&-&-1&=&-\\dfrac{3}{5}(x&-&5)&&& \\\\ \\\\\ny&+&1&=&-\\dfrac{3}{5}x&+&3&&& \\\\ \\\\\n-y&-&1&&-y&-&1&&& \\\\\n\\hline\n&&(0&=&-\\dfrac{3}{5}x&-&y&+&2)&(-5) \\\\ \\\\\n&&0&=&3x&+&5y&-&10&\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-2&=&-\\dfrac{2}{3}(x&-&-2) \\\\ \\\\\ny&+&2&=&-\\dfrac{2}{3}x&-&\\dfrac{4}{3} \\\\ \\\\\n-y&-&2&&-y&-&2 \\\\\n\\hline\n&&(0&=&-\\dfrac{2}{3}x&-&y&-&\\dfrac{10}{3})&(-3) \\\\ \\\\\n&&0&=&2x&+&3y&+&10&\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&1&=&\\dfrac{1}{2}(x&-&-4) \\\\ \\\\\ny&-&1&=&\\dfrac{1}{2}x&+&2 \\\\ \\\\\n-y&+&1&&-y&+&1 \\\\\n\\hline\n&&(0&=&\\dfrac{1}{2}x&-&y&+&3)&(2) \\\\ \\\\\n&&0&=&x&-&2y&+&6&\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-3&=&-\\dfrac{7}{4}(x&-&4) \\\\ \\\\\ny&+&3&=&-\\dfrac{7}{4}x&+&7 \\\\ \\\\\n-y&-&3&&-y&-&3 \\\\\n\\hline\n&&(0&=&-\\dfrac{7}{4}x&-&y&+&4)&(-4) \\\\ \\\\\n&&0&=&7x&+&4y&-&16&\n\\end{array}[\/latex]<\/li>\n \t
  19. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-2&=&-\\dfrac{3}{2}(x&-&4) \\\\ \\\\\ny&+&2&=&-\\dfrac{3}{2}x&+&6 \\\\ \\\\\n-y&-&2&&-y&-&2 \\\\\n\\hline\n&&(0&=&-\\dfrac{3}{2}x&-&y&+&4)&(-2) \\\\ \\\\\n&&0&=&3x&+&2y&-&8&\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&0&=&-\\dfrac{5}{2}(x&-&-2) \\\\ \\\\\n&&y&=&-\\dfrac{5}{2}x&-&5 \\\\ \\\\\n&&-y&&-y&& \\\\\n\\hline\n&&(0&=&-\\dfrac{5}{2}x&-&y&+&5)&(-2) \\\\ \\\\\n&&0&=&5x&+&2y&+&10&\n\\end{array}[\/latex]<\/li>\n \t
  21. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-3&=&-\\dfrac{2}{5}(x&-&-5) \\\\ \\\\\ny&+&3&=&-\\dfrac{2}{5}x&-&2 \\\\ \\\\\n-y&-&3&&-y&-&3 \\\\\n\\hline\n&&(0&=&-\\dfrac{2}{5}x&-&y&-&5)&(-5) \\\\ \\\\\n&&0&=&2x&+&5y&+&25&\n\\end{array}[\/latex]<\/li>\n \t
  22. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&3&=&\\dfrac{7}{3}(x&-&3) \\\\ \\\\\ny&-&3&=&\\dfrac{7}{3}x&-&7 \\\\ \\\\\n-y&+&3&&-y&+&3 \\\\\n\\hline\n&&(0&=&\\dfrac{7}{3}x&-&y&-&4)&(3) \\\\ \\\\\n&&0&=&7x&-&3y&-&12&\n\\end{array}[\/latex]<\/li>\n \t
  23. [latex]\\quad\\begin{array}[t]{rrrrlrrrr} y&-&y_1&=&m(x&-&x_1)&&\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrr}\ny&-&y_1&=&m(x&-&x_1)&& \\\\\ny&-&-2&=&1(x&-&2)&& \\\\\ny&+&2&=&x&-&2&& \\\\\n-y&-&2&&-y&-&2&& \\\\\n\\hline\n&&0&=&x&-&y&-&4\n\\end{array}[\/latex]<\/li>\n \t
  24. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&4&=&-\\dfrac{1}{3}(x&-&-3) \\\\ \\\\\ny&-&4&=&-\\dfrac{1}{3}x&-&1 \\\\ \\\\\n-y&+&4&&-y&+&4 \\\\\n\\hline\n&&(0&=&-\\dfrac{1}{3}x&-&y&+&3)&(-3) \\\\ \\\\\n&&0&=&x&+&3y&-&9&\n\\end{array}[\/latex]<\/li>\n \t
  25. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{1-3}{-3--4}\\Rightarrow \\dfrac{-2}{1}\\Rightarrow -2 [\/latex]\n[latex]\\begin{array}{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&1&=&-2(x&-&-3) \\\\\ny&-&1&=&-2x&-&6 \\\\\n&+&1&&&+&1 \\\\\n\\hline\n&&y&=&-2x&-&5\n\\end{array}[\/latex]<\/li>\n \t
  26. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-3-3}{-3-1}\\Rightarrow \\dfrac{-6}{-4}\\Rightarrow \\dfrac{3}{2}[\/latex]\n[latex]\\begin{array}{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&3&=&\\dfrac{3}{2}(x&-&1) \\\\ \\\\\ny&-&3&=&\\dfrac{3}{2}x&-&\\dfrac{3}{2} \\\\ \\\\\n&+&3&&&+&3 \\\\\n\\hline\n&&y&=&\\dfrac{3}{2}x&+&\\dfrac{3}{2}\n\\end{array}[\/latex]<\/li>\n \t
  27. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{0-1}{-3-5}\\Rightarrow \\dfrac{-1}{-8}\\Rightarrow \\dfrac{1}{8}[\/latex]\n[latex]\\begin{array}{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&0&=&\\dfrac{1}{8}(x&-&-3) \\\\ \\\\\n&&y&=&\\dfrac{1}{8}x&+&\\dfrac{3}{8}\n\\end{array}[\/latex]<\/li>\n \t
  28. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4-5}{4--4}\\Rightarrow \\dfrac{-1}{8} [\/latex]\n[latex]\\begin{array}{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&4&=&-\\dfrac{1}{8}(x&-&4) \\\\ \\\\\ny&-&4&=&-\\dfrac{1}{8}x&+&\\dfrac{1}{2} \\\\ \\\\\n&+&4&&&+&4 \\\\\n\\hline\n&&y&=&-\\dfrac{1}{8}x&+&\\dfrac{9}{2}\n\\end{array}[\/latex]<\/li>\n \t
  29. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4--2}{0--4}\\Rightarrow \\dfrac{6}{4}\\Rightarrow \\dfrac{3}{2}[\/latex]\n[latex]\\begin{array}{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&4&=&\\dfrac{3}{2}(x&-&0) \\\\ \\\\\ny&-&4&=&\\dfrac{3}{2}x&& \\\\\n&+&4&&&+&4 \\\\\n\\hline\n&&y&=&\\dfrac{3}{2}x&+&4\n\\end{array}[\/latex]<\/li>\n \t
  30. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4-1}{4--4}\\Rightarrow \\dfrac{3}{8}[\/latex]\n[latex]\\begin{array}{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&4&=&\\dfrac{3}{8}(x&-&4) \\\\ \\\\\ny&-&4&=&\\dfrac{3}{8}x&-&\\dfrac{3}{2} \\\\ \\\\\n&+&4&&&+&4 \\\\\n\\hline\n&&y&=&\\dfrac{3}{8}x&+&\\dfrac{5}{2}\n\\end{array}[\/latex]<\/li>\n \t
  31. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{3-5}{-5-3}\\Rightarrow \\dfrac{-2}{-8}\\Rightarrow \\dfrac{1}{4}[\/latex]\n[latex]\\begin{array}{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&3&=&\\dfrac{1}{4}(x&-&-5) \\\\ \\\\\ny&-&3&=&\\dfrac{1}{4}x&-&\\dfrac{5}{4} \\\\ \\\\\n&+&3&&&+&3 \\\\\n\\hline\n&&y&=&\\dfrac{1}{4}x&+&\\dfrac{17}{4}\n\\end{array}[\/latex]<\/li>\n \t
  32. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{0--4}{-5--1}\\Rightarrow \\dfrac{4}{-4}\\Rightarrow -1[\/latex]\n[latex]\\begin{array}{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&0&=&-1(x&-&-5) \\\\\n&&y&=&-x&-&5\n\\end{array}[\/latex]<\/li>\n \t
  33. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{5--3}{-4-3}\\Rightarrow \\dfrac{8}{-7}\\Rightarrow -\\dfrac{8}{7}[\/latex]\n[latex]\\begin{array}{rrrrlrrrl}\ny&-&{y}_{1}&=&m(x&-&{x}_{1})&& \\\\\ny&-&5&=&-\\dfrac{8}{7}(x&-&-4)&& \\\\ \\\\\ny&-&5&=&-\\dfrac{8}{7}x&-&\\dfrac{32}{7}&& \\\\ \\\\\n-y&+&5&&-y&+&5&& \\\\\n\\hline\n&&(0&=&-\\dfrac{8}{7}x&-&y&+&\\dfrac{3}{7}) (-7) \\\\ \\\\\n&&0&=&8x&+&7y&-&3\n\\end{array}[\/latex]<\/li>\n \t
  34. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--5}{-5--1}\\Rightarrow \\dfrac{1}{-4}\\Rightarrow -\\dfrac{1}{4}[\/latex]\n[latex]\\begin{array}{rrrrlrrrl}\ny&-&{y}_{1}&=&m(x&-&x_{1}) &&\\\\\ny&-&-5&=&-\\dfrac{1}{4}(x&-&-1) &&\\\\ \\\\\ny&+&5&=&-\\dfrac{1}{4}(x&+&1)&& \\\\ \\\\\ny&+&5&=&-\\dfrac{1}{4}x&-&\\dfrac{1}{4} &&\\\\ \\\\\n-y&-&5&&-y&-&5 &&\\\\\n\\hline\n&&(0&=&-\\dfrac{1}{4}x&-&y&-&\\dfrac{21}{4}) (-4) \\\\ \\\\\n&&0&=&x&+&4y&+&21\n\\end{array}[\/latex]<\/li>\n \t
  35. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4--3}{-2-3}\\Rightarrow \\dfrac{7}{-5}\\Rightarrow -\\dfrac{7}{5}[\/latex]\n[latex]\\begin{array}{rrrrlrrrl}\ny&-&{y}_{1}&=&m(x&-&{x}_{1}) \\\\\ny&-&4&=&-\\dfrac{7}{5}(x&-&-2) \\\\ \\\\\ny&-&4&=&-\\dfrac{7}{5}x&-&\\dfrac{14}{5} \\\\ \\\\\n-y&+&4&&-y&+&4 \\\\\n\\hline\n&&(0&=&-\\dfrac{7}{5}x&-&y&+&\\dfrac{6}{5}) (-5) \\\\ \\\\\n&&0&=&7x&+&5y&-&6\n\\end{array}[\/latex]<\/li>\n \t
  36. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--7}{-3--6}\\Rightarrow \\dfrac{3}{3}\\Rightarrow 1 [\/latex]\n[latex]\\begin{array}{rrrrlrrrr}\ny&-&y_1&=&m(x&-&x_1)&& \\\\\ny&-&-4&=&1(x&-&-3)&& \\\\\ny&+&4&=&x&+&3&& \\\\\n-y&-&4&&-y&-&4&& \\\\\n\\hline\n&&0&=&x&-&y&-&1\n\\end{array}[\/latex]<\/li>\n \t
  37. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-2-1}{-1--5}\\Rightarrow \\dfrac{-3}{4}[\/latex]\n[latex]\\begin{array}{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-2&=&-\\dfrac{3}{4}(x&-&-1) \\\\ \\\\\ny&+&2&=&-\\dfrac{3}{4}x&-&\\dfrac{3}{4} \\\\ \\\\\n-y&-&2&&-y&-&2 \\\\\n\\hline\n&&(0&=&-\\dfrac{3}{4}x&-&y&-&\\dfrac{11}{4}) &(-4) \\\\ \\\\\n&&0&=&3x&+&4y&+&11&\n\\end{array}[\/latex]<\/li>\n \t
  38. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-2--1}{5--5}\\Rightarrow \\dfrac{-1}{10}[\/latex]\n[latex]\\begin{array}{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-1&=&-\\dfrac{1}{10}(x&-&-5) \\\\ \\\\\ny&+&1&=&-\\dfrac{1}{10}x&-&\\dfrac{1}{2} \\\\ \\\\\n-y&-&1&&-y&-&1 \\\\\n\\hline\n&&(0&=&-\\dfrac{1}{10}x&-&y&-&\\dfrac{3}{2}) &(-10) \\\\ \\\\\n&&0&=&x&+&10y&+&15&\n\\end{array}[\/latex]<\/li>\n \t
  39. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-3-5}{2--5}\\Rightarrow \\dfrac{-8}{7}[\/latex]\n[latex]\\begin{array}{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-3&=&-\\dfrac{8}{7}(x&-&2) \\\\ \\\\\ny&+&3&=&-\\dfrac{8}{7}x&+&\\dfrac{16}{7} \\\\ \\\\\n-y&-&3&&-y&-&3 \\\\\n\\hline\n&&(0&=&-\\dfrac{8}{7}x&-&y&-&\\dfrac{5}{7}) &(-7) \\\\ \\\\\n&&0&=&8x&+&7y&+&5&\n\\end{array}[\/latex]<\/li>\n \t
  40. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--1}{-5-1}\\Rightarrow \\dfrac{-3}{-6}\\Rightarrow \\dfrac{1}{2}[\/latex]\n[latex]\\begin{array}{rrrrlrrrrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-1&=&\\dfrac{1}{2}(x&-&1) \\\\ \\\\\ny&+&1&=&\\dfrac{1}{2}x&-&\\dfrac{1}{2} \\\\ \\\\\n-y&-&1&&-y&-&1 \\\\\n\\hline\n&&(0&=&\\dfrac{1}{2}x&-&y&-&\\dfrac{3}{2}) &(2) \\\\ \\\\\n&&0&=&x&-&2y&-&3&\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&3&=&\\dfrac{2}{3}(x&-&2) \\\\ \\\\ y&-&3&=&\\dfrac{2}{3}x&-&\\dfrac{4}{3} \\\\ \\\\ &+&3&&&+&3 \\\\ \\hline &&y&=&\\dfrac{2}{3}x&+&\\dfrac{5}{3} \\end{array}[\/latex]<\/li>\n
    2. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&2&=&4(x&-&1) \\\\ y&-&2&=&4x&-&4 \\\\ &+&2&&&+&2 \\\\ \\hline &&y&=&4x&-&2 \\end{array}[\/latex]<\/li>\n
    3. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&2&=&\\dfrac{1}{2}(x&-&2) \\\\ \\\\ y&-&2&=&\\dfrac{1}{2}x&-&1 \\\\ &+&2&&&+&2 \\\\ \\hline &&y&=&\\dfrac{1}{2}x&+&1 \\end{array}[\/latex]<\/li>\n
    4. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&1&=&-\\dfrac{1}{2}(x&-&2) \\\\ \\\\ y&-&1&=&-\\dfrac{1}{2}x&+&1 \\\\ &+&1&&&+&1 \\\\ \\hline &&y&=&-\\dfrac{1}{2}x&+&2 \\end{array}[\/latex]<\/li>\n
    5. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-5&=&9(x&-&-1) \\\\ y&+&5&=&9x&+&9 \\\\ &-&5&&&-&5 \\\\ \\hline &&y&=&9x&+&4 \\end{array}[\/latex]<\/li>\n
    6. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-2&=&-2(x&-&2) \\\\ y&+&2&=&-2x&+&4 \\\\ &-&2&&&-&2 \\\\ \\hline &&y&=&-2x&+&2 \\end{array}[\/latex]<\/li>\n
    7. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&1&=&\\dfrac{3}{4}(x&-&-4) \\\\ \\\\ y&-&1&=&\\dfrac{3}{4}x&+&3 \\\\ &+&1&&&+&1 \\\\ \\hline &&y&=&\\dfrac{3}{4}x&+&4 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-3&=&-2(x&-&4) \\\\ y&+&3&=&-2x&+&8 \\\\ &-&3&&&-&3 \\\\ \\hline &&y&=&-2x&+&5 \\end{array}[\/latex]<\/li>\n
    9. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-2&=&-3(x&-&0) \\\\ y&+&2&=&-3x&& \\\\ &-&2&&&-&2 \\\\ \\hline &&y&=&-3x&-&2 \\\\ \\end{array}[\/latex]<\/li>\n
    10. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&1&=&4(x&-&-1) \\\\ y&-&1&=&4x&+&4 \\\\ &+&1&&&+&1 \\\\ \\hline &&y&=&4x&+&5 \\end{array}[\/latex]<\/li>\n
    11. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-5&=&-\\dfrac{1}{4}(x&-&0) \\\\ \\\\ y&+&5&=&-\\dfrac{1}{4}x&& \\\\ &-&5&&&-&5 \\\\ \\hline &&y&=&-\\dfrac{1}{4}x&-&5 \\end{array}[\/latex]<\/li>\n
    12. [latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&2&=&-\\dfrac{5}{4}(x&-&0) \\\\ \\\\ y&-&2&=&-\\dfrac{5}{4}x&& \\\\ &+&2&&&+&2 \\\\ \\hline &&y&=&-\\dfrac{5}{4}x&+&2 \\end{array}[\/latex]<\/li>\n
    13. [latex]\\begin{array}[t]{rrrrlrrrr}\\quad y&-&y_1&=&m(x&-&x_1)&&\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrr} y&-&y_1&=&m(x&-&x_1)&& \\\\ y&-&-5&=&2(x&-&-1)&& \\\\ y&+&5&=&2x&+&2&& \\\\ -y&-&5&&-y&-&5&& \\\\ \\hline &&0&=&2x&-&y&-&3 \\end{array}[\/latex]<\/li>\n
    14. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)&&&\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)&&& \\\\ y&-&-2&=&-2(x&-&2)&&& \\\\ y&+&2&=&-2x&+&4&&& \\\\ -y&-&2&&-y&-&2&&& \\\\ \\hline &&(0&=&-2x&-&y&+&2)&(-1) \\\\ &&0&=&2x&+&y&-&2& \\end{array}[\/latex]<\/li>\n
    15. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)&&&\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)&&& \\\\ y&-&-1&=&-\\dfrac{3}{5}(x&-&5)&&& \\\\ \\\\ y&+&1&=&-\\dfrac{3}{5}x&+&3&&& \\\\ \\\\ -y&-&1&&-y&-&1&&& \\\\ \\hline &&(0&=&-\\dfrac{3}{5}x&-&y&+&2)&(-5) \\\\ \\\\ &&0&=&3x&+&5y&-&10& \\end{array}[\/latex]<\/li>\n
    16. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-2&=&-\\dfrac{2}{3}(x&-&-2) \\\\ \\\\ y&+&2&=&-\\dfrac{2}{3}x&-&\\dfrac{4}{3} \\\\ \\\\ -y&-&2&&-y&-&2 \\\\ \\hline &&(0&=&-\\dfrac{2}{3}x&-&y&-&\\dfrac{10}{3})&(-3) \\\\ \\\\ &&0&=&2x&+&3y&+&10& \\end{array}[\/latex]<\/li>\n
    17. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&1&=&\\dfrac{1}{2}(x&-&-4) \\\\ \\\\ y&-&1&=&\\dfrac{1}{2}x&+&2 \\\\ \\\\ -y&+&1&&-y&+&1 \\\\ \\hline &&(0&=&\\dfrac{1}{2}x&-&y&+&3)&(2) \\\\ \\\\ &&0&=&x&-&2y&+&6& \\end{array}[\/latex]<\/li>\n
    18. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-3&=&-\\dfrac{7}{4}(x&-&4) \\\\ \\\\ y&+&3&=&-\\dfrac{7}{4}x&+&7 \\\\ \\\\ -y&-&3&&-y&-&3 \\\\ \\hline &&(0&=&-\\dfrac{7}{4}x&-&y&+&4)&(-4) \\\\ \\\\ &&0&=&7x&+&4y&-&16& \\end{array}[\/latex]<\/li>\n
    19. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-2&=&-\\dfrac{3}{2}(x&-&4) \\\\ \\\\ y&+&2&=&-\\dfrac{3}{2}x&+&6 \\\\ \\\\ -y&-&2&&-y&-&2 \\\\ \\hline &&(0&=&-\\dfrac{3}{2}x&-&y&+&4)&(-2) \\\\ \\\\ &&0&=&3x&+&2y&-&8& \\end{array}[\/latex]<\/li>\n
    20. [latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&0&=&-\\dfrac{5}{2}(x&-&-2) \\\\ \\\\ &&y&=&-\\dfrac{5}{2}x&-&5 \\\\ \\\\ &&-y&&-y&& \\\\ \\hline &&(0&=&-\\dfrac{5}{2}x&-&y&+&5)&(-2) \\\\ \\\\ &&0&=&5x&+&2y&+&10& \\end{array}[\/latex]<\/li>\n
    21. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-3&=&-\\dfrac{2}{5}(x&-&-5) \\\\ \\\\ y&+&3&=&-\\dfrac{2}{5}x&-&2 \\\\ \\\\ -y&-&3&&-y&-&3 \\\\ \\hline &&(0&=&-\\dfrac{2}{5}x&-&y&-&5)&(-5) \\\\ \\\\ &&0&=&2x&+&5y&+&25& \\end{array}[\/latex]<\/li>\n
    22. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&3&=&\\dfrac{7}{3}(x&-&3) \\\\ \\\\ y&-&3&=&\\dfrac{7}{3}x&-&7 \\\\ \\\\ -y&+&3&&-y&+&3 \\\\ \\hline &&(0&=&\\dfrac{7}{3}x&-&y&-&4)&(3) \\\\ \\\\ &&0&=&7x&-&3y&-&12& \\end{array}[\/latex]<\/li>\n
    23. [latex]\\quad\\begin{array}[t]{rrrrlrrrr} y&-&y_1&=&m(x&-&x_1)&&\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrr} y&-&y_1&=&m(x&-&x_1)&& \\\\ y&-&-2&=&1(x&-&2)&& \\\\ y&+&2&=&x&-&2&& \\\\ -y&-&2&&-y&-&2&& \\\\ \\hline &&0&=&x&-&y&-&4 \\end{array}[\/latex]<\/li>\n
    24. [latex]\\quad\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1)\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&4&=&-\\dfrac{1}{3}(x&-&-3) \\\\ \\\\ y&-&4&=&-\\dfrac{1}{3}x&-&1 \\\\ \\\\ -y&+&4&&-y&+&4 \\\\ \\hline &&(0&=&-\\dfrac{1}{3}x&-&y&+&3)&(-3) \\\\ \\\\ &&0&=&x&+&3y&-&9& \\end{array}[\/latex]<\/li>\n
    25. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{1-3}{-3--4}\\Rightarrow \\dfrac{-2}{1}\\Rightarrow -2[\/latex]
      \n[latex]\\begin{array}{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&1&=&-2(x&-&-3) \\\\ y&-&1&=&-2x&-&6 \\\\ &+&1&&&+&1 \\\\ \\hline &&y&=&-2x&-&5 \\end{array}[\/latex]<\/li>\n
    26. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-3-3}{-3-1}\\Rightarrow \\dfrac{-6}{-4}\\Rightarrow \\dfrac{3}{2}[\/latex]
      \n[latex]\\begin{array}{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&3&=&\\dfrac{3}{2}(x&-&1) \\\\ \\\\ y&-&3&=&\\dfrac{3}{2}x&-&\\dfrac{3}{2} \\\\ \\\\ &+&3&&&+&3 \\\\ \\hline &&y&=&\\dfrac{3}{2}x&+&\\dfrac{3}{2} \\end{array}[\/latex]<\/li>\n
    27. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{0-1}{-3-5}\\Rightarrow \\dfrac{-1}{-8}\\Rightarrow \\dfrac{1}{8}[\/latex]
      \n[latex]\\begin{array}{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&0&=&\\dfrac{1}{8}(x&-&-3) \\\\ \\\\ &&y&=&\\dfrac{1}{8}x&+&\\dfrac{3}{8} \\end{array}[\/latex]<\/li>\n
    28. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4-5}{4--4}\\Rightarrow \\dfrac{-1}{8}[\/latex]
      \n[latex]\\begin{array}{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&4&=&-\\dfrac{1}{8}(x&-&4) \\\\ \\\\ y&-&4&=&-\\dfrac{1}{8}x&+&\\dfrac{1}{2} \\\\ \\\\ &+&4&&&+&4 \\\\ \\hline &&y&=&-\\dfrac{1}{8}x&+&\\dfrac{9}{2} \\end{array}[\/latex]<\/li>\n
    29. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4--2}{0--4}\\Rightarrow \\dfrac{6}{4}\\Rightarrow \\dfrac{3}{2}[\/latex]
      \n[latex]\\begin{array}{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&4&=&\\dfrac{3}{2}(x&-&0) \\\\ \\\\ y&-&4&=&\\dfrac{3}{2}x&& \\\\ &+&4&&&+&4 \\\\ \\hline &&y&=&\\dfrac{3}{2}x&+&4 \\end{array}[\/latex]<\/li>\n
    30. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4-1}{4--4}\\Rightarrow \\dfrac{3}{8}[\/latex]
      \n[latex]\\begin{array}{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&4&=&\\dfrac{3}{8}(x&-&4) \\\\ \\\\ y&-&4&=&\\dfrac{3}{8}x&-&\\dfrac{3}{2} \\\\ \\\\ &+&4&&&+&4 \\\\ \\hline &&y&=&\\dfrac{3}{8}x&+&\\dfrac{5}{2} \\end{array}[\/latex]<\/li>\n
    31. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{3-5}{-5-3}\\Rightarrow \\dfrac{-2}{-8}\\Rightarrow \\dfrac{1}{4}[\/latex]
      \n[latex]\\begin{array}{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&3&=&\\dfrac{1}{4}(x&-&-5) \\\\ \\\\ y&-&3&=&\\dfrac{1}{4}x&-&\\dfrac{5}{4} \\\\ \\\\ &+&3&&&+&3 \\\\ \\hline &&y&=&\\dfrac{1}{4}x&+&\\dfrac{17}{4} \\end{array}[\/latex]<\/li>\n
    32. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{0--4}{-5--1}\\Rightarrow \\dfrac{4}{-4}\\Rightarrow -1[\/latex]
      \n[latex]\\begin{array}{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&0&=&-1(x&-&-5) \\\\ &&y&=&-x&-&5 \\end{array}[\/latex]<\/li>\n
    33. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{5--3}{-4-3}\\Rightarrow \\dfrac{8}{-7}\\Rightarrow -\\dfrac{8}{7}[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrl} y&-&{y}_{1}&=&m(x&-&{x}_{1})&& \\\\ y&-&5&=&-\\dfrac{8}{7}(x&-&-4)&& \\\\ \\\\ y&-&5&=&-\\dfrac{8}{7}x&-&\\dfrac{32}{7}&& \\\\ \\\\ -y&+&5&&-y&+&5&& \\\\ \\hline &&(0&=&-\\dfrac{8}{7}x&-&y&+&\\dfrac{3}{7}) (-7) \\\\ \\\\ &&0&=&8x&+&7y&-&3 \\end{array}[\/latex]<\/li>\n
    34. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--5}{-5--1}\\Rightarrow \\dfrac{1}{-4}\\Rightarrow -\\dfrac{1}{4}[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrl} y&-&{y}_{1}&=&m(x&-&x_{1}) &&\\\\ y&-&-5&=&-\\dfrac{1}{4}(x&-&-1) &&\\\\ \\\\ y&+&5&=&-\\dfrac{1}{4}(x&+&1)&& \\\\ \\\\ y&+&5&=&-\\dfrac{1}{4}x&-&\\dfrac{1}{4} &&\\\\ \\\\ -y&-&5&&-y&-&5 &&\\\\ \\hline &&(0&=&-\\dfrac{1}{4}x&-&y&-&\\dfrac{21}{4}) (-4) \\\\ \\\\ &&0&=&x&+&4y&+&21 \\end{array}[\/latex]<\/li>\n
    35. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{4--3}{-2-3}\\Rightarrow \\dfrac{7}{-5}\\Rightarrow -\\dfrac{7}{5}[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrl} y&-&{y}_{1}&=&m(x&-&{x}_{1}) \\\\ y&-&4&=&-\\dfrac{7}{5}(x&-&-2) \\\\ \\\\ y&-&4&=&-\\dfrac{7}{5}x&-&\\dfrac{14}{5} \\\\ \\\\ -y&+&4&&-y&+&4 \\\\ \\hline &&(0&=&-\\dfrac{7}{5}x&-&y&+&\\dfrac{6}{5}) (-5) \\\\ \\\\ &&0&=&7x&+&5y&-&6 \\end{array}[\/latex]<\/li>\n
    36. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--7}{-3--6}\\Rightarrow \\dfrac{3}{3}\\Rightarrow 1[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrr} y&-&y_1&=&m(x&-&x_1)&& \\\\ y&-&-4&=&1(x&-&-3)&& \\\\ y&+&4&=&x&+&3&& \\\\ -y&-&4&&-y&-&4&& \\\\ \\hline &&0&=&x&-&y&-&1 \\end{array}[\/latex]<\/li>\n
    37. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-2-1}{-1--5}\\Rightarrow \\dfrac{-3}{4}[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-2&=&-\\dfrac{3}{4}(x&-&-1) \\\\ \\\\ y&+&2&=&-\\dfrac{3}{4}x&-&\\dfrac{3}{4} \\\\ \\\\ -y&-&2&&-y&-&2 \\\\ \\hline &&(0&=&-\\dfrac{3}{4}x&-&y&-&\\dfrac{11}{4}) &(-4) \\\\ \\\\ &&0&=&3x&+&4y&+&11& \\end{array}[\/latex]<\/li>\n
    38. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-2--1}{5--5}\\Rightarrow \\dfrac{-1}{10}[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-1&=&-\\dfrac{1}{10}(x&-&-5) \\\\ \\\\ y&+&1&=&-\\dfrac{1}{10}x&-&\\dfrac{1}{2} \\\\ \\\\ -y&-&1&&-y&-&1 \\\\ \\hline &&(0&=&-\\dfrac{1}{10}x&-&y&-&\\dfrac{3}{2}) &(-10) \\\\ \\\\ &&0&=&x&+&10y&+&15& \\end{array}[\/latex]<\/li>\n
    39. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-3-5}{2--5}\\Rightarrow \\dfrac{-8}{7}[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-3&=&-\\dfrac{8}{7}(x&-&2) \\\\ \\\\ y&+&3&=&-\\dfrac{8}{7}x&+&\\dfrac{16}{7} \\\\ \\\\ -y&-&3&&-y&-&3 \\\\ \\hline &&(0&=&-\\dfrac{8}{7}x&-&y&-&\\dfrac{5}{7}) &(-7) \\\\ \\\\ &&0&=&8x&+&7y&+&5& \\end{array}[\/latex]<\/li>\n
    40. [latex]m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{-4--1}{-5-1}\\Rightarrow \\dfrac{-3}{-6}\\Rightarrow \\dfrac{1}{2}[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-1&=&\\dfrac{1}{2}(x&-&1) \\\\ \\\\ y&+&1&=&\\dfrac{1}{2}x&-&\\dfrac{1}{2} \\\\ \\\\ -y&-&1&&-y&-&1 \\\\ \\hline &&(0&=&\\dfrac{1}{2}x&-&y&-&\\dfrac{3}{2}) &(2) \\\\ \\\\ &&0&=&x&-&2y&-&3& \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":27,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1650","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1650","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1650\/revisions"}],"predecessor-version":[{"id":1651,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1650\/revisions\/1651"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1650\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1650"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1650"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1650"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1650"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}