{"id":1318,"date":"2019-06-14T13:15:29","date_gmt":"2019-06-14T17:15:29","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1318"},"modified":"2020-01-04T15:41:22","modified_gmt":"2020-01-04T20:41:22","slug":"answer-key-3-4","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-3-4\/","title":{"raw":"Answer Key 3.4","rendered":"Answer Key 3.4"},"content":{"raw":"[latexpage]\r\nFor questions 1 to 10, sketch the linear equation using the slope intercept method.\r\n
    \r\n \t
  1. \\(y = -\\dfrac{1}{4}x - 3\\)\"Graph<\/li>\r\n \t
  2. \\(y = \\dfrac{3}{2}x - 1\\)\u00a0 \u00a0 \u00a0\"Graph<\/li>\r\n \t
  3. \\(y = -\\dfrac{5}{4}x - 4\\)\u00a0 \u00a0 \u00a0 \u00a0\"Line<\/li>\r\n \t
  4. \\(y = -\\dfrac{3}{5}x + 1\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
  5. \\(y = -\\dfrac{4}{3}x + 2\\)\u00a0 \u00a0 \u00a0 \u00a0\"Graph<\/li>\r\n \t
  6. \\(y = \\dfrac{5}{3}x + 4\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n \t
  7. \\(y = \\dfrac{3}{2}x - 5\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
  8. \\(y = -\\dfrac{2}{3}x - 2\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n \t
  9. \\(y = -\\dfrac{4}{5}x - 3\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n \t
  10. \\(y = \\dfrac{1}{2}x\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n<\/ol>\r\nFor questions 11 to 20, sketch the linear equation using the \\(x\\) and \\(y\\) intercepts.\r\n
      \r\n \t
    1. \\(x + 4y = -4\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
    2. \\(2x - y = 2\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n \t
    3. \\(2x + y = 4\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n \t
    4. \\(3x + 4y = 12\\)\u00a0 \u00a0\"Line<\/li>\r\n \t
    5. \\(2x - y = 2\\)\u00a0 \u00a0\"Line<\/li>\r\n \t
    6. \\(4x + 3y = -12\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
    7. \\(x + y = -5\\)\u00a0 \u00a0\"Line<\/li>\r\n \t
    8. \\(3x + 2y = 6\\)\u00a0 \u00a0\"Line<\/li>\r\n \t
    9. \\(x - y = -2\\)\u00a0 \u00a0\"Line<\/li>\r\n \t
    10. \\(4x - y = -4\\)\u00a0 \u00a0\"Line<\/li>\r\n<\/ol>\r\nFor questions 21 to 28, sketch the linear equation using any method.\r\n
        \r\n \t
      1. \\(y = -\\dfrac{1}{2}x + 3\\)\u00a0 \u00a0\"Line<\/li>\r\n \t
      2. \\(y = 2x - 1\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
      3. \\(y = -\\dfrac{5}{4}x\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
      4. \\(y = -3x + 2\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
      5. \\(y = -\\dfrac{3}{2}x + 1\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
      6. \\(y = \\dfrac{1}{3}x - 3\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n \t
      7. \\(y = \\dfrac{3}{2}x + 2\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n \t
      8. \\(y = 2x - 2\\)\u00a0 \u00a0 \u00a0\"Line<\/li>\r\n<\/ol>\r\n
          \r\n \t
        1. \\(\\begin{array}{rrrrrrr}\r\ny& +& 3& =& -\\dfrac{4}{5}x& +& 3 \\\\\r\n&-&3&&&-&3 \\\\\r\n\\midrule\r\n&&y&=&-\\dfrac{4}{5}x&&\r\n\\end{array}\\)\"Line<\/li>\r\n \t
        2. \\(\\begin{array}{rrrrrrr}\r\ny&-&4&=&\\dfrac{1}{2}x&& \\\\\r\n&+&4&&&+&4 \\\\\r\n\\midrule\r\n&&y&=&\\dfrac{1}{2}x&+&4\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
        3. \\(\\begin{array}{rrrrrrr}\r\nx& +& 5y& =& -3& +& 2y \\\\\r\n-x&-&2y&&-x&-&2y \\\\\r\n\\midrule\r\n&&3y&=&-x&-&3 \\\\\r\n&&y&=&-\\dfrac{1}{3}x&-&1\r\n\\end{array}\\)\u00a0 \u00a0\"Line<\/li>\r\n \t
        4. \\(\\begin{array}{rrrrrrrrr}\r\n3x& -& y& =& 4& +& x& -& 2y \\\\\r\n-3x&+&2y&&&-&3x&+&2y \\\\\r\n\\midrule\r\n&&y&=&-2x&+&4&&\r\n\\end{array}\\)\u00a0 \u00a0\"Line<\/li>\r\n \t
        5. \\(\\begin{array}{rrrrrrrr}\r\n4x&+&3y&=&5(x&+&y)& \\\\\r\n4x&+&3y&=&5x&+&5y& \\\\\r\n-4x&-&5y&&-4x&-&5y& \\\\\r\n\\midrule\r\n&&\\dfrac{-2y}{-2}&=&\\dfrac{x}{-2}&&& \\\\ \\\\\r\n&&y&=&-\\dfrac{1}{2}x&&&\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
        6. \\(\\begin{array}{rrrrrrr}\r\n3x&+&4y&=&12&-&2y \\\\\r\n-3x&+&2y&&-3x&+&2y \\\\\r\n\\midrule\r\n&&\\dfrac{6y}{6}&=&\\dfrac{-3x}{6}&+&\\dfrac{12}{6} \\\\ \\\\\r\n&&y&=&-\\dfrac{1}{2}x&+&2\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
        7. \\(\\begin{array}{rrrrrrr}\r\n2x&-&y&=&2&-&y \\\\\r\n&+&y&&&+&y \\\\\r\n\\midrule\r\n&&2x&=&2&& \\\\\r\n&&x&=&1&&\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
        8. \\(\\begin{array}{rrrrrrrrr}\r\n7x&+&3y&=&2(2x&+&2y)&+&6 \\\\\r\n7x&+&3y&=&4x&+&4y&+&6 \\\\\r\n-7x&-&4y&&-7x&-&4y&& \\\\\r\n\\midrule\r\n&&-y&=&-3x&+&6&& \\\\\r\n&&y&=&3x&-&6&&\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
        9. \\(\\begin{array}{rrrrrrr}\r\nx&+&y&=&-2x&+&3 \\\\\r\n-x&&&&-\\phantom{1}x&& \\\\\r\n\\midrule\r\n&&y&=&-3x&+&3\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
        10. \\(\\begin{array}{rrrrrrr}\r\n3x&+&4y&=&3y&+&6 \\\\\r\n-3x&-&3y&&-3y&-&3x \\\\\r\n\\midrule\r\n&&y&=&-3x&+&6\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
        11. \\(\\begin{array}{rrrrrrrrr}\r\n2(x&+&y)&=&-3(x&+&y)&+&5 \\\\\r\n2x&+&2y&=&-3x&-&3y&+&5 \\\\\r\n-2x&+&3y&&-2x&+&3y&& \\\\\r\n\\midrule\r\n&&5y&=&-5x&+&5&& \\\\\r\n&&y&=&-x&+&1&&\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n \t
        12. \\(\\begin{array}{rrrrrrr}\r\n9x&-&y&=&4x&+&5 \\\\\r\n-9x&&&&-9x&& \\\\\r\n\\midrule\r\n&&-y&=&-5x&+&5 \\\\\r\n&&y&=&5x&-&5\r\n\\end{array}\\)\u00a0 \u00a0\u00a0\"Line<\/li>\r\n<\/ol>","rendered":"

          For questions 1 to 10, sketch the linear equation using the slope intercept method.<\/p>\n

            \n
          1. \"y = -\dfrac{1}{4}x - 3\"\"Graph<\/li>\n
          2. \"y = \dfrac{3}{2}x - 1\"\u00a0 \u00a0 \u00a0\"Graph<\/li>\n
          3. \"y = -\dfrac{5}{4}x - 4\"\u00a0 \u00a0 \u00a0 \u00a0\"Line<\/li>\n
          4. \"y = -\dfrac{3}{5}x + 1\"\u00a0 \u00a0\u00a0\"Line<\/li>\n
          5. \"y = -\dfrac{4}{3}x + 2\"\u00a0 \u00a0 \u00a0 \u00a0\"Graph<\/li>\n
          6. \"y = \dfrac{5}{3}x + 4\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n
          7. \"y = \dfrac{3}{2}x - 5\"\u00a0 \u00a0\u00a0\"Line<\/li>\n
          8. \"y = -\dfrac{2}{3}x - 2\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n
          9. \"y = -\dfrac{4}{5}x - 3\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n
          10. \"y = \dfrac{1}{2}x\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n<\/ol>\n

            For questions 11 to 20, sketch the linear equation using the \"x\" and \"y\" intercepts.<\/p>\n

              \n
            1. \"x + 4y = -4\"\u00a0 \u00a0\u00a0\"Line<\/li>\n
            2. \"2x - y = 2\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n
            3. \"2x + y = 4\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n
            4. \"3x + 4y = 12\"\u00a0 \u00a0\"Line<\/li>\n
            5. \"2x - y = 2\"\u00a0 \u00a0\"Line<\/li>\n
            6. \"4x + 3y = -12\"\u00a0 \u00a0\u00a0\"Line<\/li>\n
            7. \"x + y = -5\"\u00a0 \u00a0\"Line<\/li>\n
            8. \"3x + 2y = 6\"\u00a0 \u00a0\"Line<\/li>\n
            9. \"x - y = -2\"\u00a0 \u00a0\"Line<\/li>\n
            10. \"4x - y = -4\"\u00a0 \u00a0\"Line<\/li>\n<\/ol>\n

              For questions 21 to 28, sketch the linear equation using any method.<\/p>\n

                \n
              1. \"y = -\dfrac{1}{2}x + 3\"\u00a0 \u00a0\"Line<\/li>\n
              2. \"y = 2x - 1\"\u00a0 \u00a0\u00a0\"Line<\/li>\n
              3. \"y = -\dfrac{5}{4}x\"\u00a0 \u00a0\u00a0\"Line<\/li>\n
              4. \"y = -3x + 2\"\u00a0 \u00a0\u00a0\"Line<\/li>\n
              5. \"y = -\dfrac{3}{2}x + 1\"\u00a0 \u00a0\u00a0\"Line<\/li>\n
              6. \"y = \dfrac{1}{3}x - 3\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n
              7. \"y = \dfrac{3}{2}x + 2\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n
              8. \"y = 2x - 2\"\u00a0 \u00a0 \u00a0\"Line<\/li>\n<\/ol>\n
                  \n
                1. \"\begin{array}{rrrrrrr}\"Line<\/li>\n
                2. \"\begin{array}{rrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n
                3. \"\begin{array}{rrrrrrr}\u00a0 \u00a0\"Line<\/li>\n
                4. \"\begin{array}{rrrrrrrrr}\u00a0 \u00a0\"Line<\/li>\n
                5. \"\begin{array}{rrrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n
                6. \"\begin{array}{rrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n
                7. \"\begin{array}{rrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n
                8. \"\begin{array}{rrrrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n
                9. \"\begin{array}{rrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n
                10. \"\begin{array}{rrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n
                11. \"\begin{array}{rrrrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n
                12. \"\begin{array}{rrrrrrr}\u00a0 \u00a0\u00a0\"Line<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":21,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1318","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1318","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":19,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1318\/revisions"}],"predecessor-version":[{"id":3773,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1318\/revisions\/3773"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1318\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1318"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1318"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1318"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}