Answer Key 3.4

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

  1. y = -\dfrac{1}{4}x - 3Graph 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 \\ \midrule &&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 \\ \midrule &&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 \\ \midrule &&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 \\ \midrule &&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& \\ \midrule &&\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 \\ \midrule &&\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 \\ \midrule &&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&& \\ \midrule &&-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&& \\ \midrule &&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 \\ \midrule &&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&& \\ \midrule &&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&& \\ \midrule &&-y&=&-5x&+&5 \\ &&y&=&5x&-&5 \end{array}    Line on graph passes through (0,-5) (1,0), (2,5)

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