{"id":1652,"date":"2021-12-02T19:38:55","date_gmt":"2021-12-03T00:38:55","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-6\/"},"modified":"2022-11-02T10:37:07","modified_gmt":"2022-11-02T14:37:07","slug":"answer-key-3-6","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-6\/","title":{"raw":"Answer Key 3.6","rendered":"Answer Key 3.6"},"content":{"raw":"
    \n \t
  1. [latex]m=2[\/latex]<\/li>\n \t
  2. [latex]m=-\\dfrac{2}{3}[\/latex]<\/li>\n \t
  3. [latex]m=4[\/latex]<\/li>\n \t
  4. [latex]m=-10[\/latex]<\/li>\n \t
  5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrr}\nx&-&y&=&4&&& \\\\\n-x&&&&-x&&& \\\\\n\\hline\n&&(-y&=&-x&+&4)&(-1) \\\\\n&&y&=&x&-&4& \\\\\n&&m&=&1&&&\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrrr}\n6x&-&5y&=&20&&& \\\\\n-6x&&&&-6x&&& \\\\\n\\hline\n&&\\dfrac{-5y}{-5}&=&\\dfrac{-6x}{-5}&+&\\dfrac{20}{-5}& \\\\ \\\\\n&&y&=&\\dfrac{6}{5}x&-&4& \\\\ \\\\\n&&m&=&\\dfrac{6}{5}&&&\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrlrrr}\ny&=&\\dfrac{1}{3}x&&& \\\\ \\\\\n\\therefore m&=&\\dfrac{1}{3} &&& \\\\\nm_{\\perp} &=&-1&\\div &\\dfrac{1}{3}&\\text{or} \\\\\nm_{\\perp}&=&-3 &&&\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{lrlrrrr}\nm&=&-\\dfrac{1}{2} &&&& \\\\\nm_{\\perp} &=&-1&\\div &-\\dfrac{1}{2}&&\\\\ \\\\\nm_{\\perp}&=&-1 &\\cdot &-\\dfrac{2}{1}&=& 2\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{lrlrrrr}\nm&=&-\\dfrac{1}{3} &&&& \\\\\nm_{\\perp} &=&-1&\\div &-\\dfrac{1}{3}&&\\\\ \\\\\nm_{\\perp}&=&-1 &\\cdot &-\\dfrac{3}{1}&=& 3\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{lrlrrrr}\nm&=&\\dfrac{4}{5} &&&& \\\\\nm_{\\perp} &=&-1&\\div &\\dfrac{4}{5}&&\\\\ \\\\\nm_{\\perp}&=&-1 &\\cdot &\\dfrac{5}{4}&=& -\\dfrac{5}{4}\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\nx&-&3y&=&-6& \\\\\n-x&&&&-x&& \\\\\n\\hline\n&&\\dfrac{-3y}{-3}&=&\\dfrac{-x}{-3}&-&\\dfrac{6}{-3} \\\\ \\\\\n&&y&=&\\dfrac{1}{3}x&+&2 \\\\\n&&m_{\\perp}&=&-1&\\div &\\dfrac{1}{3} \\\\\n&&m_{\\perp}&=&-3&&\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n3x&-&y&=&-3& \\\\\n-3x&&&&-3x&& \\\\\n\\hline\n&&-y&=&-3x&-&3 \\\\\n&&y&=&3x&+&3 \\\\\n&&m_{\\perp}&=&-1&\\div &3 \\\\\n&&m_{\\perp}&=&-\\dfrac{1}{3}&&\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\begin{array}[t]{rrr}m&=&\\dfrac{2}{5}\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&4&=&\\dfrac{2}{5}(x&-&1) \\\\ \\\\\ny&-&4&=&\\dfrac{2}{5}x&-&\\dfrac{2}{5} \\\\ \\\\\n&+&4&&&+&4 \\\\\n\\hline\n&&y&=&\\dfrac{2}{5}x&+&\\dfrac{18}{5}\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\begin{array}[t]{rrr}m&=&-3\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&2&=&-3(x&-&5) \\\\\ny&-&2&=&-3x&+&15 \\\\\n&+&2&&&+&2 \\\\\n\\hline\n&&y&=&-3x&+&17\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\begin{array}[t]{rrrr}m&=&\\dfrac{1}{2}\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&4&=&\\dfrac{1}{2}(x&-&3) \\\\ \\\\\ny&-&4&=&\\dfrac{1}{2}x&-&\\dfrac{3}{2} \\\\ \\\\\n&+&4&&&+&4 \\\\\n\\hline\n&&y&=&\\dfrac{1}{2}x&+&\\dfrac{5}{2}\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\begin{array}[t]{rrrr}m&=&\\dfrac{4}{3}\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&-1&=&\\dfrac{4}{3}(x&-&1) \\\\ \\\\\ny&+&1&=&\\dfrac{4}{3}x&-&\\dfrac{4}{3} \\\\ \\\\\n&-&1&&&-&1 \\\\\n\\hline\n&&y&=&\\dfrac{4}{3}x&-&\\dfrac{7}{3}\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\begin{array}[t]{rrr}m&=&-\\dfrac{3}{5}\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&3&=&-\\dfrac{3}{5}(x&-&2) \\\\ \\\\\ny&-&3&=&-\\dfrac{3}{5}x&+&\\dfrac{6}{5} \\\\ \\\\\n&+&3&&&+&3 \\\\\n\\hline\n&&y&=&-\\dfrac{3}{5}x&+&\\dfrac{21}{5}\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]\\begin{array}[t]{rrr}m&=&\\dfrac{1}{3}\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\ny&-&y_1&=&m(x&-&x_1) \\\\\ny&-&3&=&\\dfrac{1}{3}(x&-&-1) \\\\ \\\\\ny&-&3&=&\\dfrac{1}{3}x&+&\\dfrac{1}{3} \\\\ \\\\\n&+&3&&&+&3 \\\\\n\\hline\n&&y&=&\\dfrac{1}{3}x&+&\\dfrac{10}{3}\n\\end{array}[\/latex]<\/li>\n \t
  19. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n-x&+&y&=&1&&&& \\\\\n+x&&&&+x&&&& \\\\\n\\hline\n&&y&=&x&+&1&& \\\\\n&&\\therefore m&=&1&&&& \\\\ \\\\\ny&-&y_1&=&m(x&-&x_1)&& \\\\\ny&-&-5&=&1(x&-&1)&& \\\\\ny&+&5&=&x&-&1&& \\\\\n-y&-&5&&-y&-&5&& \\\\\n\\hline\n&&0&=&x&-&y&-&6\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n-x&+&2y&=&2&&& \\\\\n+x&&&&+x&&& \\\\\n\\hline\n&&2y&=&x&+&2& \\\\\n&\\text{or}&y&=&\\dfrac{1}{2}x&+&1& \\\\ \\\\\n&&\\therefore m&=&-2&&& \\\\ \\\\\ny&-&y_1&=&m(x&-&x_1)& \\\\\ny&-&-2&=&-2(x&-&1)& \\\\\ny&+&2&=&-2x&+&2& \\\\\n-y&-&2&&-y&-&2& \\\\\n\\hline\n&&(0&=&-2x&-&y)&(-1) \\\\\n&&0&=&2x&+&y&\n\\end{array}[\/latex]<\/li>\n \t
  21. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrr}\n5x&+&y&=&-3&&&&& \\\\\n-5x&&&&-5x&&&&& \\\\\n\\hline\n&&y&=&-5x&-&3&&& \\\\\n&&\\therefore m&=&-5&&&&& \\\\ \\\\\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\ny&-&2&=&-5(x&-&5)&&& \\\\\ny&-&2&=&-5x&+&25&&& \\\\\n-y&+&2&&-y&+&2&&& \\\\\n\\hline\n&&(0&=&-5x&-&y&+&27)&(-1) \\\\\n&&0&=&5x&+&y&-&27&\n\\end{array}[\/latex]<\/li>\n \t
  22. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrr}\n-x&+&y&=&1&&&&& \\\\\n+x&&&&+x&&&&& \\\\\n\\hline\n&&y&=&x&+&1&&& \\\\\n&&\\therefore m&=&-1&&&&& \\\\ \\\\\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\ny&-&3&=&-1(x&-&1)&&& \\\\\ny&-&3&=&-x&+&1&&& \\\\\n-y&+&3&&-y&+&3&&& \\\\\n\\hline\n&&(0&=&-x&-&y&+&4)&(-1) \\\\\n&&0&=&x&+&y&-&4&\n\\end{array}[\/latex]<\/li>\n \t
  23. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n-4x&+&y&=&0&&&& \\\\\n+4x&&&&+4x&&&& \\\\\n\\hline\n&&y&=&4x&&&& \\\\\n&&\\therefore m&=&4&&&& \\\\ \\\\\ny&-&y_1&=&m(x&-&x_1)&& \\\\\ny&-&2&=&4(x&-&4)&& \\\\\ny&-&2&=&4x&-&16&& \\\\\n-y&+&2&&-y&+&2&& \\\\\n\\hline\n&&0&=&4x&-&y&-&14\n\\end{array}[\/latex]<\/li>\n \t
  24. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrr}\n3x&+&7y&=&0&&&&& \\\\\n-3x&&&&-3x&&&&& \\\\\n\\hline\n&&7y&=&-3x&&&&& \\\\\n&\\text{or}&y&=&-\\dfrac{3}{7}x&&&&& \\\\ \\\\\n&&\\therefore m&=&\\dfrac{7}{3}&&&&& \\\\ \\\\\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\ny&-&-5&=&\\dfrac{7}{3}(x&-&-3)&&& \\\\ \\\\\ny&+&5&=&\\dfrac{7}{3}x&+&7&&& \\\\ \\\\\n-y&-&5&&-y&-&5&&& \\\\\n\\hline\n&&(0&=&\\dfrac{7}{3}x&-&y&+&2)&(3) \\\\ \\\\\n&&0&=&7x&-&3y&+&6&\n\\end{array}[\/latex]<\/li>\n \t
  25. [latex]y=-3[\/latex]<\/li>\n \t
  26. [latex]x=-5[\/latex]<\/li>\n \t
  27. [latex]x=-3[\/latex]<\/li>\n \t
  28. [latex]y=0[\/latex]<\/li>\n \t
  29. [latex]y=-1[\/latex]<\/li>\n \t
  30. [latex]x=2[\/latex]<\/li>\n \t
  31. [latex]x=-2[\/latex]<\/li>\n \t
  32. [latex]y=-4[\/latex]<\/li>\n \t
  33. [latex]y=3[\/latex]<\/li>\n \t
  34. [latex]x=-3[\/latex]<\/li>\n \t
  35. [latex]x=5[\/latex]<\/li>\n \t
  36. [latex]y=-1[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]m=2[\/latex]<\/li>\n
    2. [latex]m=-\\dfrac{2}{3}[\/latex]<\/li>\n
    3. [latex]m=4[\/latex]<\/li>\n
    4. [latex]m=-10[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrr} x&-&y&=&4&&& \\\\ -x&&&&-x&&& \\\\ \\hline &&(-y&=&-x&+&4)&(-1) \\\\ &&y&=&x&-&4& \\\\ &&m&=&1&&& \\end{array}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrrr} 6x&-&5y&=&20&&& \\\\ -6x&&&&-6x&&& \\\\ \\hline &&\\dfrac{-5y}{-5}&=&\\dfrac{-6x}{-5}&+&\\dfrac{20}{-5}& \\\\ \\\\ &&y&=&\\dfrac{6}{5}x&-&4& \\\\ \\\\ &&m&=&\\dfrac{6}{5}&&& \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlrrr} y&=&\\dfrac{1}{3}x&&& \\\\ \\\\ \\therefore m&=&\\dfrac{1}{3} &&& \\\\ m_{\\perp} &=&-1&\\div &\\dfrac{1}{3}&\\text{or} \\\\ m_{\\perp}&=&-3 &&& \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{lrlrrrr} m&=&-\\dfrac{1}{2} &&&& \\\\ m_{\\perp} &=&-1&\\div &-\\dfrac{1}{2}&&\\\\ \\\\ m_{\\perp}&=&-1 &\\cdot &-\\dfrac{2}{1}&=& 2 \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{lrlrrrr} m&=&-\\dfrac{1}{3} &&&& \\\\ m_{\\perp} &=&-1&\\div &-\\dfrac{1}{3}&&\\\\ \\\\ m_{\\perp}&=&-1 &\\cdot &-\\dfrac{3}{1}&=& 3 \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{lrlrrrr} m&=&\\dfrac{4}{5} &&&& \\\\ m_{\\perp} &=&-1&\\div &\\dfrac{4}{5}&&\\\\ \\\\ m_{\\perp}&=&-1 &\\cdot &\\dfrac{5}{4}&=& -\\dfrac{5}{4} \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} x&-&3y&=&-6& \\\\ -x&&&&-x&& \\\\ \\hline &&\\dfrac{-3y}{-3}&=&\\dfrac{-x}{-3}&-&\\dfrac{6}{-3} \\\\ \\\\ &&y&=&\\dfrac{1}{3}x&+&2 \\\\ &&m_{\\perp}&=&-1&\\div &\\dfrac{1}{3} \\\\ &&m_{\\perp}&=&-3&& \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 3x&-&y&=&-3& \\\\ -3x&&&&-3x&& \\\\ \\hline &&-y&=&-3x&-&3 \\\\ &&y&=&3x&+&3 \\\\ &&m_{\\perp}&=&-1&\\div &3 \\\\ &&m_{\\perp}&=&-\\dfrac{1}{3}&& \\end{array}[\/latex]<\/li>\n
    13. [latex]\\begin{array}[t]{rrr}m&=&\\dfrac{2}{5}\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&4&=&\\dfrac{2}{5}(x&-&1) \\\\ \\\\ y&-&4&=&\\dfrac{2}{5}x&-&\\dfrac{2}{5} \\\\ \\\\ &+&4&&&+&4 \\\\ \\hline &&y&=&\\dfrac{2}{5}x&+&\\dfrac{18}{5} \\end{array}[\/latex]<\/li>\n
    14. [latex]\\begin{array}[t]{rrr}m&=&-3\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&2&=&-3(x&-&5) \\\\ y&-&2&=&-3x&+&15 \\\\ &+&2&&&+&2 \\\\ \\hline &&y&=&-3x&+&17 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\begin{array}[t]{rrrr}m&=&\\dfrac{1}{2}\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&4&=&\\dfrac{1}{2}(x&-&3) \\\\ \\\\ y&-&4&=&\\dfrac{1}{2}x&-&\\dfrac{3}{2} \\\\ \\\\ &+&4&&&+&4 \\\\ \\hline &&y&=&\\dfrac{1}{2}x&+&\\dfrac{5}{2} \\end{array}[\/latex]<\/li>\n
    16. [latex]\\begin{array}[t]{rrrr}m&=&\\dfrac{4}{3}\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&-1&=&\\dfrac{4}{3}(x&-&1) \\\\ \\\\ y&+&1&=&\\dfrac{4}{3}x&-&\\dfrac{4}{3} \\\\ \\\\ &-&1&&&-&1 \\\\ \\hline &&y&=&\\dfrac{4}{3}x&-&\\dfrac{7}{3} \\end{array}[\/latex]<\/li>\n
    17. [latex]\\begin{array}[t]{rrr}m&=&-\\dfrac{3}{5}\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&3&=&-\\dfrac{3}{5}(x&-&2) \\\\ \\\\ y&-&3&=&-\\dfrac{3}{5}x&+&\\dfrac{6}{5} \\\\ \\\\ &+&3&&&+&3 \\\\ \\hline &&y&=&-\\dfrac{3}{5}x&+&\\dfrac{21}{5} \\end{array}[\/latex]<\/li>\n
    18. [latex]\\begin{array}[t]{rrr}m&=&\\dfrac{1}{3}\\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} y&-&y_1&=&m(x&-&x_1) \\\\ y&-&3&=&\\dfrac{1}{3}(x&-&-1) \\\\ \\\\ y&-&3&=&\\dfrac{1}{3}x&+&\\dfrac{1}{3} \\\\ \\\\ &+&3&&&+&3 \\\\ \\hline &&y&=&\\dfrac{1}{3}x&+&\\dfrac{10}{3} \\end{array}[\/latex]<\/li>\n
    19. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} -x&+&y&=&1&&&& \\\\ +x&&&&+x&&&& \\\\ \\hline &&y&=&x&+&1&& \\\\ &&\\therefore m&=&1&&&& \\\\ \\\\ y&-&y_1&=&m(x&-&x_1)&& \\\\ y&-&-5&=&1(x&-&1)&& \\\\ y&+&5&=&x&-&1&& \\\\ -y&-&5&&-y&-&5&& \\\\ \\hline &&0&=&x&-&y&-&6 \\end{array}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrr} -x&+&2y&=&2&&& \\\\ +x&&&&+x&&& \\\\ \\hline &&2y&=&x&+&2& \\\\ &\\text{or}&y&=&\\dfrac{1}{2}x&+&1& \\\\ \\\\ &&\\therefore m&=&-2&&& \\\\ \\\\ y&-&y_1&=&m(x&-&x_1)& \\\\ y&-&-2&=&-2(x&-&1)& \\\\ y&+&2&=&-2x&+&2& \\\\ -y&-&2&&-y&-&2& \\\\ \\hline &&(0&=&-2x&-&y)&(-1) \\\\ &&0&=&2x&+&y& \\end{array}[\/latex]<\/li>\n
    21. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrr} 5x&+&y&=&-3&&&&& \\\\ -5x&&&&-5x&&&&& \\\\ \\hline &&y&=&-5x&-&3&&& \\\\ &&\\therefore m&=&-5&&&&& \\\\ \\\\ y&-&y_1&=&m(x&-&x_1)&&& \\\\ y&-&2&=&-5(x&-&5)&&& \\\\ y&-&2&=&-5x&+&25&&& \\\\ -y&+&2&&-y&+&2&&& \\\\ \\hline &&(0&=&-5x&-&y&+&27)&(-1) \\\\ &&0&=&5x&+&y&-&27& \\end{array}[\/latex]<\/li>\n
    22. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrr} -x&+&y&=&1&&&&& \\\\ +x&&&&+x&&&&& \\\\ \\hline &&y&=&x&+&1&&& \\\\ &&\\therefore m&=&-1&&&&& \\\\ \\\\ y&-&y_1&=&m(x&-&x_1)&&& \\\\ y&-&3&=&-1(x&-&1)&&& \\\\ y&-&3&=&-x&+&1&&& \\\\ -y&+&3&&-y&+&3&&& \\\\ \\hline &&(0&=&-x&-&y&+&4)&(-1) \\\\ &&0&=&x&+&y&-&4& \\end{array}[\/latex]<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} -4x&+&y&=&0&&&& \\\\ +4x&&&&+4x&&&& \\\\ \\hline &&y&=&4x&&&& \\\\ &&\\therefore m&=&4&&&& \\\\ \\\\ y&-&y_1&=&m(x&-&x_1)&& \\\\ y&-&2&=&4(x&-&4)&& \\\\ y&-&2&=&4x&-&16&& \\\\ -y&+&2&&-y&+&2&& \\\\ \\hline &&0&=&4x&-&y&-&14 \\end{array}[\/latex]<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrr} 3x&+&7y&=&0&&&&& \\\\ -3x&&&&-3x&&&&& \\\\ \\hline &&7y&=&-3x&&&&& \\\\ &\\text{or}&y&=&-\\dfrac{3}{7}x&&&&& \\\\ \\\\ &&\\therefore m&=&\\dfrac{7}{3}&&&&& \\\\ \\\\ y&-&y_1&=&m(x&-&x_1)&&& \\\\ y&-&-5&=&\\dfrac{7}{3}(x&-&-3)&&& \\\\ \\\\ y&+&5&=&\\dfrac{7}{3}x&+&7&&& \\\\ \\\\ -y&-&5&&-y&-&5&&& \\\\ \\hline &&(0&=&\\dfrac{7}{3}x&-&y&+&2)&(3) \\\\ \\\\ &&0&=&7x&-&3y&+&6& \\end{array}[\/latex]<\/li>\n
    25. [latex]y=-3[\/latex]<\/li>\n
    26. [latex]x=-5[\/latex]<\/li>\n
    27. [latex]x=-3[\/latex]<\/li>\n
    28. [latex]y=0[\/latex]<\/li>\n
    29. [latex]y=-1[\/latex]<\/li>\n
    30. [latex]x=2[\/latex]<\/li>\n
    31. [latex]x=-2[\/latex]<\/li>\n
    32. [latex]y=-4[\/latex]<\/li>\n
    33. [latex]y=3[\/latex]<\/li>\n
    34. [latex]x=-3[\/latex]<\/li>\n
    35. [latex]x=5[\/latex]<\/li>\n
    36. [latex]y=-1[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":28,"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-1652","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\/1652","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\/1652\/revisions"}],"predecessor-version":[{"id":1653,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1652\/revisions\/1653"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1652\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1652"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1652"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1652"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1652"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}