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Answer Key 3.4

For questions 1 to 10, sketch the linear equation using the slope intercept method.

  1. \(y = -\dfrac{1}{4}x - 3\)Graph with line that passes through -4,-2) (0,-3), (4,4)
  2. \(y = \dfrac{3}{2}x - 1\)     Graph with line that passes through at (-2,-4), (0,-1), (2,2), (4,5)
  3. \(y = -\dfrac{5}{4}x - 4\)       Line through graph that passees through (-5,1), (0,-4)
  4. \(y = -\dfrac{3}{5}x + 1\)    Line on graph passes through (-5,-4), (0,1), (5,-2)
  5. \(y = -\dfrac{4}{3}x + 2\)       Graph with line passes through (-3,6), (0,2), (3,-2)
  6. \(y = \dfrac{5}{3}x + 4\)     Line on graph passes through (-3,-1), (0,5)
  7. \(y = \dfrac{3}{2}x - 5\)    Line on graph passes through (0,-5), (-2,-2), (4,1)
  8. \(y = -\dfrac{2}{3}x - 2\)     Line on graph passes trhough (-3,0), (0,-2), (3,-4)
  9. \(y = -\dfrac{4}{5}x - 3\)     Line on graph passes through (-5,1), (0,-3)
  10. \(y = \dfrac{1}{2}x\)     Line on graph passes through (-4,-2), (-2,-1), (0,0), (2,1), (2,4)

For questions 11 to 20, sketch the linear equation using the \(x\) and \(y\) intercepts.

  1. \(x + 4y = -4\)    Line on graph passees through (-4,0), (0,-1)
  2. \(2x - y = 2\)     Line on graph passes through (0,-2), (1,0)
  3. \(2x + y = 4\)     Line on graph passes through (0,4), (2,0)
  4. \(3x + 4y = 12\)   Line on graph passees through (0,3), (4,0)
  5. \(2x - y = 2\)   Line on graph passes through (0,-2), (1,0)
  6. \(4x + 3y = -12\)    Line on graph passes through (-3,0) and (0,-4)
  7. \(x + y = -5\)   Line on graph passes through (-5,0) and (0,-5)
  8. \(3x + 2y = 6\)   Line on graph passes through (0,3) (2,0)
  9. \(x - y = -2\)   Line on graph passes through (-2,0), (0,2)
  10. \(4x - y = -4\)   Line on graph passes through (-1,0), (0,4)

For questions 21 to 28, sketch the linear equation using any method.

  1. \(y = -\dfrac{1}{2}x + 3\)   Line on graph passess through (-4,-5), (-2,-4), (0,3), (2,2), (4,1)
  2. \(y = 2x - 1\)    Line on graph passes through (0,-1), (1,1), (2,3)
  3. \(y = -\dfrac{5}{4}x\)    Line on graph passes through (-4,5), (0,0)
  4. \(y = -3x + 2\)    Line on graph passes through (-1,5) (0,2), (-1,-1), (2,-4)
  5. \(y = -\dfrac{3}{2}x + 1\)    Line on graph passes through (0,1), (2,-2), (4,-4_
  6. \(y = \dfrac{1}{3}x - 3\)     Line on graph passes through (0,-3), (3,-2), (5, -1)
  7. \(y = \dfrac{3}{2}x + 2\)     Line on graph passes through (-2,-1), (0,2), (2,4)
  8. \(y = 2x - 2\)     Line on graph passes through (0,2), (1,0), (2,2), (3,4)
  1. \(\begin{array}{rrrrrrr}
    y& +& 3& =& -\dfrac{4}{5}x& +& 3 \\
    &-&3&&&-&3 \\
    \hline
    &&y&=&-\dfrac{4}{5}x&&
    \end{array}\)Line on graph passes through (-5,4), (0,0), (5, -4)
  2. \(\begin{array}{rrrrrrr}
    y&-&4&=&\dfrac{1}{2}x&& \\
    &+&4&&&+&4 \\
    \hline
    &&y&=&\dfrac{1}{2}x&+&4
    \end{array}\)    Line on graph passes through (-6,1), (-4,2), (-2,3), (0,4), (2,5), (4,6)
  3. \(\begin{array}{rrrrrrr}
    x& +& 5y& =& -3& +& 2y \\
    -x&-&2y&&-x&-&2y \\
    \hline
    &&3y&=&-x&-&3 \\
    &&y&=&-\dfrac{1}{3}x&-&1
    \end{array}\)   Line on graph passes through (-6,1), (3,0), (0,-1), (3,-2)
  4. \(\begin{array}{rrrrrrrrr}
    3x& -& y& =& 4& +& x& -& 2y \\
    -3x&+&2y&&&-&3x&+&2y \\
    \hline
    &&y&=&-2x&+&4&&
    \end{array}\)   Line on graph passes through (-1,6), (0,4), (1,2), (2,0), (3,-2), (4,-4), (-5,-5)
  5. \(\begin{array}{rrrrrrrr}
    4x&+&3y&=&5(x&+&y)& \\
    4x&+&3y&=&5x&+&5y& \\
    -4x&-&5y&&-4x&-&5y& \\
    \hline
    &&\dfrac{-2y}{-2}&=&\dfrac{x}{-2}&&& \\ \\
    &&y&=&-\dfrac{1}{2}x&&&
    \end{array}\)    Line on graph passes through (0,0), (2,-1), (4,-2), (6,-3)
  6. \(\begin{array}{rrrrrrr}
    3x&+&4y&=&12&-&2y \\
    -3x&+&2y&&-3x&+&2y \\
    \hline
    &&\dfrac{6y}{6}&=&\dfrac{-3x}{6}&+&\dfrac{12}{6} \\ \\
    &&y&=&-\dfrac{1}{2}x&+&2
    \end{array}\)    Line on graph passes through (0,2), (2,1), (4,0), (6,-1)
  7. \(\begin{array}{rrrrrrr}
    2x&-&y&=&2&-&y \\
    &+&y&&&+&y \\
    \hline
    &&2x&=&2&& \\
    &&x&=&1&&
    \end{array}\)    Line on graph passes through (2,5), (2,4), (2,3)...(2,-1), (2,-2)
  8. \(\begin{array}{rrrrrrrrr}
    7x&+&3y&=&2(2x&+&2y)&+&6 \\
    7x&+&3y&=&4x&+&4y&+&6 \\
    -7x&-&4y&&-7x&-&4y&& \\
    \hline
    &&-y&=&-3x&+&6&& \\
    &&y&=&3x&-&6&&
    \end{array}\)    Line on graph passes through (0,-6), (1,-3), (0,2), (3,3), (5,6)
  9. \(\begin{array}{rrrrrrr}
    x&+&y&=&-2x&+&3 \\
    -x&&&&-\phantom{1}x&& \\
    \hline
    &&y&=&-3x&+&3
    \end{array}\)    Line on graph passes through (0,3), (1,0), (2,-3)
  10. \(\begin{array}{rrrrrrr}
    3x&+&4y&=&3y&+&6 \\
    -3x&-&3y&&-3y&-&3x \\
    \hline
    &&y&=&-3x&+&6
    \end{array}\)    Line on graph passes through (0,6), (1,3), (2,0), 3,-3), (4,-6)
  11. \(\begin{array}{rrrrrrrrr}
    2(x&+&y)&=&-3(x&+&y)&+&5 \\
    2x&+&2y&=&-3x&-&3y&+&5 \\
    -2x&+&3y&&-2x&+&3y&& \\
    \hline
    &&5y&=&-5x&+&5&& \\
    &&y&=&-x&+&1&&
    \end{array}\)    Line on graph passes through (0,1), 0,1), (2,-1), (3,-2), (4,3), (5,4)
  12. \(\begin{array}{rrrrrrr}
    9x&-&y&=&4x&+&5 \\
    -9x&&&&-9x&& \\
    \hline
    &&-y&=&-5x&+&5 \\
    &&y&=&5x&-&5
    \end{array}\)    Line on graph passes through (0,-5) (1,0), (2,5)

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