{"id":1648,"date":"2021-12-02T19:38:54","date_gmt":"2021-12-03T00:38:54","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-4\/"},"modified":"2022-11-02T10:37:05","modified_gmt":"2022-11-02T14:37:05","slug":"answer-key-3-4","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-4\/","title":{"raw":"Answer Key 3.4","rendered":"Answer Key 3.4"},"content":{"raw":"For questions 1 to 10, sketch the linear equation using the slope intercept method.\n
    \n \t
  1. [latex]y = -\\dfrac{1}{4}x - 3[\/latex]\n\"Graph<\/li>\n \t
  2. [latex]y = \\dfrac{3}{2}x - 1[\/latex]\n\"Graph<\/li>\n \t
  3. [latex]y = -\\dfrac{5}{4}x - 4[\/latex]\n\"Line<\/li>\n \t
  4. [latex]y = -\\dfrac{3}{5}x + 1[\/latex]\n\"Line<\/li>\n \t
  5. [latex]y = -\\dfrac{4}{3}x + 2[\/latex]\n\"Graph<\/li>\n \t
  6. [latex]y = \\dfrac{5}{3}x + 4[\/latex]\n\"Line<\/li>\n \t
  7. [latex]y = \\dfrac{3}{2}x - 5[\/latex]\n\"Line<\/li>\n \t
  8. [latex]y = -\\dfrac{2}{3}x - 2[\/latex]\n\"Line<\/li>\n \t
  9. [latex]y = -\\dfrac{4}{5}x - 3[\/latex]\n\"Line<\/li>\n \t
  10. [latex]y = \\dfrac{1}{2}x[\/latex]\n\"Line<\/li>\n<\/ol>\nFor questions 11 to 20, sketch the linear equation using the [latex]x[\/latex] and [latex]y[\/latex] intercepts.\n
      \n \t
    1. [latex]x + 4y = -4[\/latex]\n\"Line<\/li>\n \t
    2. [latex]2x - y = 2[\/latex]\n\"Line<\/li>\n \t
    3. [latex]2x + y = 4[\/latex]\n\"Line<\/li>\n \t
    4. [latex]3x + 4y = 12[\/latex]\n\"Line<\/li>\n \t
    5. [latex]2x - y = 2[\/latex]\n\"Line<\/li>\n \t
    6. [latex]4x + 3y = -12[\/latex]\n\"Line<\/li>\n \t
    7. [latex]x + y = -5[\/latex]\n\"Line<\/li>\n \t
    8. [latex]3x + 2y = 6[\/latex]\n\"Line<\/li>\n \t
    9. [latex]x - y = -2[\/latex]\n\"Line<\/li>\n \t
    10. [latex]4x - y = -4[\/latex]\n\"Line<\/li>\n<\/ol>\nFor questions 21 to 28, sketch the linear equation using any method.\n
        \n \t
      1. [latex]y = -\\dfrac{1}{2}x + 3[\/latex]\n\"Line<\/li>\n \t
      2. [latex]y = 2x - 1[\/latex]\n\"Line<\/li>\n \t
      3. [latex]y = -\\dfrac{5}{4}x[\/latex]\n\"Line<\/li>\n \t
      4. [latex]y = -3x + 2[\/latex]\n\"Line<\/li>\n \t
      5. [latex]y = -\\dfrac{3}{2}x + 1[\/latex]\n\"Line<\/li>\n \t
      6. [latex]y = \\dfrac{1}{3}x - 3[\/latex]\n\"Line<\/li>\n \t
      7. [latex]y = \\dfrac{3}{2}x + 2[\/latex]\n\"Line<\/li>\n \t
      8. [latex]y = 2x - 2[\/latex]\n\"Line<\/li>\n<\/ol>\n
          \n \t
        1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\ny& +& 3& =& -\\dfrac{4}{5}x& +& 3 \\\\\n&-&3&&&-&3 \\\\\n\\hline\n&&y&=&-\\dfrac{4}{5}x&&\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\ny&-&4&=&\\dfrac{1}{2}x&& \\\\\n&+&4&&&+&4 \\\\\n\\hline\n&&y&=&\\dfrac{1}{2}x&+&4\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\nx& +& 5y& =& -3& +& 2y \\\\\n-x&-&2y&&-x&-&2y \\\\\n\\hline\n&&3y&=&-x&-&3 \\\\\n&&y&=&-\\dfrac{1}{3}x&-&1\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n3x& -& y& =& 4& +& x& -& 2y \\\\\n-3x&+&2y&&&-&3x&+&2y \\\\\n\\hline\n&&y&=&-2x&+&4&&\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n4x&+&3y&=&5(x&+&y)& \\\\\n4x&+&3y&=&5x&+&5y& \\\\\n-4x&-&5y&&-4x&-&5y& \\\\\n\\hline\n&&\\dfrac{-2y}{-2}&=&\\dfrac{x}{-2}&&& \\\\ \\\\\n&&y&=&-\\dfrac{1}{2}x&&&\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n3x&+&4y&=&12&-&2y \\\\\n-3x&+&2y&&-3x&+&2y \\\\\n\\hline\n&&\\dfrac{6y}{6}&=&\\dfrac{-3x}{6}&+&\\dfrac{12}{6} \\\\ \\\\\n&&y&=&-\\dfrac{1}{2}x&+&2\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n2x&-&y&=&2&-&y \\\\\n&+&y&&&+&y \\\\\n\\hline\n&&2x&=&2&& \\\\\n&&x&=&1&&\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n7x&+&3y&=&2(2x&+&2y)&+&6 \\\\\n7x&+&3y&=&4x&+&4y&+&6 \\\\\n-7x&-&4y&&-7x&-&4y&& \\\\\n\\hline\n&&-y&=&-3x&+&6&& \\\\\n&&y&=&3x&-&6&&\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\nx&+&y&=&-2x&+&3 \\\\\n-x&&&&-\\phantom{1}x&& \\\\\n\\hline\n&&y&=&-3x&+&3\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n3x&+&4y&=&3y&+&6 \\\\\n-3x&-&3y&&-3y&-&3x \\\\\n\\hline\n&&y&=&-3x&+&6\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n2(x&+&y)&=&-3(x&+&y)&+&5 \\\\\n2x&+&2y&=&-3x&-&3y&+&5 \\\\\n-2x&+&3y&&-2x&+&3y&& \\\\\n\\hline\n&&5y&=&-5x&+&5&& \\\\\n&&y&=&-x&+&1&&\n\\end{array}[\/latex]\n\"Line<\/li>\n \t
        12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n9x&-&y&=&4x&+&5 \\\\\n-9x&&&&-9x&& \\\\\n\\hline\n&&-y&=&-5x&+&5 \\\\\n&&y&=&5x&-&5\n\\end{array}[\/latex]\n\"Line<\/li>\n<\/ol>","rendered":"

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

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

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

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

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

                \n
              1. [latex]y = -\\dfrac{1}{2}x + 3[\/latex]
                \n\"Line<\/li>\n
              2. [latex]y = 2x - 1[\/latex]
                \n\"Line<\/li>\n
              3. [latex]y = -\\dfrac{5}{4}x[\/latex]
                \n\"Line<\/li>\n
              4. [latex]y = -3x + 2[\/latex]
                \n\"Line<\/li>\n
              5. [latex]y = -\\dfrac{3}{2}x + 1[\/latex]
                \n\"Line<\/li>\n
              6. [latex]y = \\dfrac{1}{3}x - 3[\/latex]
                \n\"Line<\/li>\n
              7. [latex]y = \\dfrac{3}{2}x + 2[\/latex]
                \n\"Line<\/li>\n
              8. [latex]y = 2x - 2[\/latex]
                \n\"Line<\/li>\n<\/ol>\n
                  \n
                1. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrr} y& +& 3& =& -\\dfrac{4}{5}x& +& 3 \\\\ &-&3&&&-&3 \\\\ \\hline &&y&=&-\\dfrac{4}{5}x&& \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                2. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrr} y&-&4&=&\\dfrac{1}{2}x&& \\\\ &+&4&&&+&4 \\\\ \\hline &&y&=&\\dfrac{1}{2}x&+&4 \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                3. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrr} x& +& 5y& =& -3& +& 2y \\\\ -x&-&2y&&-x&-&2y \\\\ \\hline &&3y&=&-x&-&3 \\\\ &&y&=&-\\dfrac{1}{3}x&-&1 \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                4. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrrrr} 3x& -& y& =& 4& +& x& -& 2y \\\\ -3x&+&2y&&&-&3x&+&2y \\\\ \\hline &&y&=&-2x&+&4&& \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                5. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrrr} 4x&+&3y&=&5(x&+&y)& \\\\ 4x&+&3y&=&5x&+&5y& \\\\ -4x&-&5y&&-4x&-&5y& \\\\ \\hline &&\\dfrac{-2y}{-2}&=&\\dfrac{x}{-2}&&& \\\\ \\\\ &&y&=&-\\dfrac{1}{2}x&&& \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                6. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrr} 3x&+&4y&=&12&-&2y \\\\ -3x&+&2y&&-3x&+&2y \\\\ \\hline &&\\dfrac{6y}{6}&=&\\dfrac{-3x}{6}&+&\\dfrac{12}{6} \\\\ \\\\ &&y&=&-\\dfrac{1}{2}x&+&2 \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                7. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrr} 2x&-&y&=&2&-&y \\\\ &+&y&&&+&y \\\\ \\hline &&2x&=&2&& \\\\ &&x&=&1&& \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                8. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrrrr} 7x&+&3y&=&2(2x&+&2y)&+&6 \\\\ 7x&+&3y&=&4x&+&4y&+&6 \\\\ -7x&-&4y&&-7x&-&4y&& \\\\ \\hline &&-y&=&-3x&+&6&& \\\\ &&y&=&3x&-&6&& \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                9. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrr} x&+&y&=&-2x&+&3 \\\\ -x&&&&-\\phantom{1}x&& \\\\ \\hline &&y&=&-3x&+&3 \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                10. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrr} 3x&+&4y&=&3y&+&6 \\\\ -3x&-&3y&&-3y&-&3x \\\\ \\hline &&y&=&-3x&+&6 \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                11. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrrrr} 2(x&+&y)&=&-3(x&+&y)&+&5 \\\\ 2x&+&2y&=&-3x&-&3y&+&5 \\\\ -2x&+&3y&&-2x&+&3y&& \\\\ \\hline &&5y&=&-5x&+&5&& \\\\ &&y&=&-x&+&1&& \\end{array}[\/latex]
                  \n\"Line<\/li>\n
                12. [latex]\\phantom{a}[\/latex]
                  \n[latex]\\begin{array}[t]{rrrrrrr} 9x&-&y&=&4x&+&5 \\\\ -9x&&&&-9x&& \\\\ \\hline &&-y&=&-5x&+&5 \\\\ &&y&=&5x&-&5 \\end{array}[\/latex]
                  \n\"Line<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":26,"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-1648","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\/1648","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\/1648\/revisions"}],"predecessor-version":[{"id":1649,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1648\/revisions\/1649"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1648\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1648"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1648"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1648"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}