{"id":1340,"date":"2019-06-17T14:16:58","date_gmt":"2019-06-17T18:16:58","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1340"},"modified":"2019-11-04T13:00:30","modified_gmt":"2019-11-04T18:00:30","slug":"answer-key-3-6","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-3-6\/","title":{"raw":"Answer Key 3.6","rendered":"Answer Key 3.6"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(m=2\\)<\/li>\r\n \t
  2. \\(m=-\\dfrac{2}{3}\\)<\/li>\r\n \t
  3. \\(m=4\\)<\/li>\r\n \t
  4. \\(m=-10\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrrrlrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\nx&-&y&=&4&&& \\\\\r\n-x&&&&-x&&& \\\\\r\n\\midrule\r\n&&(-y&=&-x&+&4)&(-1) \\\\\r\n&&y&=&x&-&4& \\\\\r\n&&m&=&1&&&\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrrrlrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n6x&-&5y&=&20&&& \\\\\r\n-6x&&&&-6x&&& \\\\\r\n\\midrule\r\n&&\\dfrac{-5y}{-5}&=&\\dfrac{-6x}{-5}&+&\\dfrac{20}{-5}& \\\\ \\\\\r\n&&y&=&\\dfrac{6}{5}x&-&4& \\\\ \\\\\r\n&&m&=&\\dfrac{6}{5}&&&\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrlrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\ny&=&\\dfrac{1}{3}x&&& \\\\ \\\\\r\n\\therefore m&=&\\dfrac{1}{3} &&& \\\\\r\nm_{\\perp} &=&-1&\\div &\\dfrac{1}{3}&\\text{or} \\\\\r\nm_{\\perp}&=&-3 &&&\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{lrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\nm&=&-\\dfrac{1}{2} &&&& \\\\\r\nm_{\\perp} &=&-1&\\div &-\\dfrac{1}{2}&&\\\\ \\\\\r\nm_{\\perp}&=&-1 &\\cdot &-\\dfrac{2}{1}&=& 2\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{lrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\nm&=&-\\dfrac{1}{3} &&&& \\\\\r\nm_{\\perp} &=&-1&\\div &-\\dfrac{1}{3}&&\\\\ \\\\\r\nm_{\\perp}&=&-1 &\\cdot &-\\dfrac{3}{1}&=& 3\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{lrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\nm&=&\\dfrac{4}{5} &&&& \\\\\r\nm_{\\perp} &=&-1&\\div &\\dfrac{4}{5}&&\\\\ \\\\\r\nm_{\\perp}&=&-1 &\\cdot &\\dfrac{5}{4}&=& -\\dfrac{5}{4}\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx&-&3y&=&-6& \\\\\r\n-x&&&&-x&& \\\\\r\n\\midrule\r\n&&\\dfrac{-3y}{-3}&=&\\dfrac{-x}{-3}&-&\\dfrac{6}{-3} \\\\ \\\\\r\n&&y&=&\\dfrac{1}{3}x&+&2 \\\\\r\n&&m_{\\perp}&=&-1&\\div &\\dfrac{1}{3} \\\\\r\n&&m_{\\perp}&=&-3&&\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&-&y&=&-3& \\\\\r\n-3x&&&&-3x&& \\\\\r\n\\midrule\r\n&&-y&=&-3x&-&3 \\\\\r\n&&y&=&3x&+&3 \\\\\r\n&&m_{\\perp}&=&-1&\\div &3 \\\\\r\n&&m_{\\perp}&=&-\\dfrac{1}{3}&&\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nm&=&\\dfrac{2}{5}&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&4&=&\\dfrac{2}{5}(x&-&1) \\\\ \\\\\r\ny&-&4&=&\\dfrac{2}{5}x&-&\\dfrac{2}{5} \\\\ \\\\\r\n&+&4&&&+&4 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{2}{5}x&+&\\dfrac{18}{5}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nm&=&-3&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&2&=&-3(x&-&5) \\\\\r\ny&-&2&=&-3x&+&15 \\\\\r\n&+&2&&&+&2 \\\\\r\n\\midrule\r\n&&y&=&-3x&+&17\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nm&=&\\dfrac{1}{2}&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&4&=&\\dfrac{1}{2}(x&-&3) \\\\ \\\\\r\ny&-&4&=&\\dfrac{1}{2}x&-&\\dfrac{3}{2} \\\\ \\\\\r\n&+&4&&&+&4 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{1}{2}x&+&\\dfrac{5}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nm&=&\\dfrac{4}{3}&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&-1&=&\\dfrac{4}{3}(x&-&1) \\\\ \\\\\r\ny&+&1&=&\\dfrac{4}{3}x&-&\\dfrac{4}{3} \\\\ \\\\\r\n&-&1&&&-&1 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{4}{3}x&-&\\dfrac{7}{3}\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nm&=&-\\dfrac{3}{5}&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&3&=&-\\dfrac{3}{5}(x&-&2) \\\\ \\\\\r\ny&-&3&=&-\\dfrac{3}{5}x&+&\\dfrac{6}{5} \\\\ \\\\\r\n&+&3&&&+&3 \\\\\r\n\\midrule\r\n&&y&=&-\\dfrac{3}{5}x&+&\\dfrac{21}{5}\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nm&=&\\dfrac{1}{3}&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1) \\\\\r\ny&-&3&=&\\dfrac{1}{3}(x&-&-1) \\\\ \\\\\r\ny&-&3&=&\\dfrac{1}{3}x&+&\\dfrac{1}{3} \\\\ \\\\\r\n&+&3&&&+&3 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{1}{3}x&+&\\dfrac{10}{3}\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-x&+&y&=&1&&&& \\\\\r\n+x&&&&+x&&&& \\\\\r\n\\midrule\r\n&&y&=&x&+&1&& \\\\\r\n&&\\therefore m&=&1&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&& \\\\\r\ny&-&-5&=&1(x&-&1)&& \\\\\r\ny&+&5&=&x&-&1&& \\\\\r\n-y&-&5&&-y&-&5&& \\\\\r\n\\midrule\r\n&&0&=&x&-&y&-&6\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-x&+&2y&=&2&&& \\\\\r\n+x&&&&+x&&& \\\\\r\n\\midrule\r\n&&2y&=&x&+&2& \\\\\r\n&\\text{or}&y&=&\\dfrac{1}{2}x&+&1& \\\\ \\\\\r\n&&\\therefore m&=&-2&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)& \\\\\r\ny&-&-2&=&-2(x&-&1)& \\\\\r\ny&+&2&=&-2x&+&2& \\\\\r\n-y&-&2&&-y&-&2& \\\\\r\n\\midrule\r\n&&(0&=&-2x&-&y)&(-1) \\\\\r\n&&0&=&2x&+&y&\r\n\\end{array}\\)<\/li>\r\n \t
  21. \\(\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n5x&+&y&=&-3&&&&& \\\\\r\n-5x&&&&-5x&&&&& \\\\\r\n\\midrule\r\n&&y&=&-5x&-&3&&& \\\\\r\n&&\\therefore m&=&-5&&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\r\ny&-&2&=&-5(x&-&5)&&& \\\\\r\ny&-&2&=&-5x&+&25&&& \\\\\r\n-y&+&2&&-y&+&2&&& \\\\\r\n\\midrule\r\n&&(0&=&-5x&-&y&+&27)&(-1) \\\\\r\n&&0&=&5x&+&y&-&27&\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-x&+&y&=&1&&&&& \\\\\r\n+x&&&&+x&&&&& \\\\\r\n\\midrule\r\n&&y&=&x&+&1&&& \\\\\r\n&&\\therefore m&=&-1&&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\r\ny&-&3&=&-1(x&-&1)&&& \\\\\r\ny&-&3&=&-x&+&1&&& \\\\\r\n-y&+&3&&-y&+&3&&& \\\\\r\n\\midrule\r\n&&(0&=&-x&-&y&+&4)&(-1) \\\\\r\n&&0&=&x&+&y&-&4&\r\n\\end{array}\\)<\/li>\r\n \t
  23. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-4x&+&y&=&0&&&& \\\\\r\n+4x&&&&+4x&&&& \\\\\r\n\\midrule\r\n&&y&=&4x&&&& \\\\\r\n&&\\therefore m&=&4&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&& \\\\\r\ny&-&2&=&4(x&-&4)&& \\\\\r\ny&-&2&=&4x&-&16&& \\\\\r\n-y&+&2&&-y&+&2&& \\\\\r\n\\midrule\r\n&&0&=&4x&-&y&-&14\r\n\\end{array}\\)<\/li>\r\n \t
  24. \\(\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&+&7y&=&0&&&&& \\\\\r\n-3x&&&&-3x&&&&& \\\\\r\n\\midrule\r\n&&7y&=&-3x&&&&& \\\\\r\n&\\text{or}&y&=&-\\dfrac{3}{7}x&&&&& \\\\ \\\\\r\n&&\\therefore m&=&\\dfrac{7}{3}&&&&& \\\\ \\\\\r\ny&-&y_1&=&m(x&-&x_1)&&& \\\\\r\ny&-&-5&=&\\dfrac{7}{3}(x&-&-3)&&& \\\\ \\\\\r\ny&+&5&=&\\dfrac{7}{3}x&+&7&&& \\\\ \\\\\r\n-y&-&5&&-y&-&5&&& \\\\\r\n\\midrule\r\n&&(0&=&\\dfrac{7}{3}x&-&y&+&2)&(3) \\\\ \\\\\r\n&&0&=&7x&-&3y&+&6&\r\n\\end{array}\\)<\/li>\r\n \t
  25. \\(y=-3\\)<\/li>\r\n \t
  26. \\(x=-5\\)<\/li>\r\n \t
  27. \\(x=-3\\)<\/li>\r\n \t
  28. \\(y=0\\)<\/li>\r\n \t
  29. \\(y=-1\\)<\/li>\r\n \t
  30. \\(x=2\\)<\/li>\r\n \t
  31. \\(x=-2\\)<\/li>\r\n \t
  32. \\(y=-4\\)<\/li>\r\n \t
  33. \\(y=3\\)<\/li>\r\n \t
  34. \\(x=-3\\)<\/li>\r\n \t
  35. \\(x=5\\)<\/li>\r\n \t
  36. \\(y=-1\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"m=2\"<\/li>\n
    2. \"m=-\dfrac{2}{3}\"<\/li>\n
    3. \"m=4\"<\/li>\n
    4. \"m=-10\"<\/li>\n
    5. \"\begin{array}{rrrrlrrr}<\/li>\n
    6. \"\begin{array}{rrrrlrrr}<\/li>\n
    7. \"\begin{array}{rrlrrr}<\/li>\n
    8. \"\begin{array}{lrlrrrr}<\/li>\n
    9. \"\begin{array}{lrlrrrr}<\/li>\n
    10. \"\begin{array}{lrlrrrr}<\/li>\n
    11. \"\begin{array}{rrrrlrr}<\/li>\n
    12. \"\begin{array}{rrrrrrr}<\/li>\n
    13. \"\begin{array}{rrrrlrr}<\/li>\n
    14. \"\begin{array}{rrrrlrr}<\/li>\n
    15. \"\begin{array}{rrrrlrr}<\/li>\n
    16. \"\begin{array}{rrrrlrr}<\/li>\n
    17. \"\begin{array}{rrrrlrr}<\/li>\n
    18. \"\begin{array}{rrrrlrr}<\/li>\n
    19. \"\begin{array}{rrrrrrrrr}<\/li>\n
    20. \"\begin{array}{rrrrrrrr}<\/li>\n
    21. \"\begin{array}{rrrrrrrrrr}<\/li>\n
    22. \"\begin{array}{rrrrrrrrrr}<\/li>\n
    23. \"\begin{array}{rrrrrrrrr}<\/li>\n
    24. \"\begin{array}{rrrrrrrrrr}<\/li>\n
    25. \"y=-3\"<\/li>\n
    26. \"x=-5\"<\/li>\n
    27. \"x=-3\"<\/li>\n
    28. \"y=0\"<\/li>\n
    29. \"y=-1\"<\/li>\n
    30. \"x=2\"<\/li>\n
    31. \"x=-2\"<\/li>\n
    32. \"y=-4\"<\/li>\n
    33. \"y=3\"<\/li>\n
    34. \"x=-3\"<\/li>\n
    35. \"x=5\"<\/li>\n
    36. \"y=-1\"<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":23,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1340","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1340","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":7,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1340\/revisions"}],"predecessor-version":[{"id":2961,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1340\/revisions\/2961"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1340\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1340"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1340"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1340"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}