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Parallel and Perpendicular Lines

discia.org 10 questions · 22 marks
Name Date
  1. Either paper 3 marks

    Here are four lines on a square grid.

    xyABCD
    (a)

    Which two lines are parallel?

    Line ____ and line ____

    (b)

    Here is a different grid.

    xy-2-1123123450

    There are four points on this grid that each have both coordinates that are whole numbers and \(x\)-coordinate \(+\) \(y\)-coordinate \(= 5\)

    Plot the four points on the grid.

    Show answer
    (a) Line A and line C
    (b) Points at \((0, 5)\), \((1, 4)\), \((2, 3)\) and \((3, 2)\)
    (b)xy-2-1123123450
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  2. Either paper 1 mark

    Write down the equation of a straight line parallel to \(y = -\frac{1}{3}x + 1\)

    Show answer
    \(y = -\frac{1}{3}x + k\) for any number \(k\) other than \(1\), for example \(y = -\frac{1}{3}x - 1\)
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  3. Either paper Higher2 marks
    (a)

    The line \(L\) has equation \(y = 4x + 5\)

    State the gradient of a line that is perpendicular to \(L\).

    (b)

    A different line has gradient \(\frac{2}{3}\)

    Work out the gradient of a line perpendicular to that line.

    Show answer
    (a) \(-\frac{1}{4}\)
    (b) \(-\frac{3}{2}\)
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  4. Either paper 2 marks
    (a)

    Write down the equation of a straight line that is parallel to \(y + 3x = -6\)

    (b)

    A straight line

    - has gradient \(3\) - passes through the point \((-3, -2)\)

    Circle the equation of the line.

    \(y = 3x - 2\)

    \(y = 3x\)

    \(y = -4x - 14\)

    \(y = 3x + 7\)

    Show answer
    (a) \(y = -3x + 6\) (any line \(y = -3x + k\) with \(k \neq -6\))
    (b) \(y = 3x + 7\)
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  5. Either paper Higher2 marks

    Here are the equations of two straight lines.

    \(y = 2x - 2\)

    \(y = 2x - 5\)

    Are the two lines parallel, perpendicular or neither?

    You must show your working.

    Show answer
    Parallel
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  6. Either paper Higher2 marks

    The lines \(y = -2x + 6\) and \(y = \frac{1}{2}x - 4\) are both drawn on the grid.

    xy-8-6-4-22468-10-9-8-7-6-5-4-3-2123456789100

    Are the two lines perpendicular?

    You must show your working.

    Show answer
    Yes
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  7. Either paper 2 marks

    Here are the equations of two straight lines.

    \(y = \frac{ 7 }{ 3 }x - 9\)

    \(9y = 21x - 2\)

    Grace says that these lines are parallel.

    Is Grace correct?

    You must give a reason for your answer.

    Show answer
    Yes: the first line has gradient \(\frac{7}{3}\) and the second line has gradient \(\frac{7}{3}\)
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  8. Either paper Higher3 marks

    The line \(L\) has equation \(y = 2x + 2\)

    Find an equation of the line that is perpendicular to \(L\) and passes through the point \((4, -4)\).

    Give your answer in the form \(y = mx + c\).

    Show answer
    \(y = -\frac{1}{2}x - 2\)
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  9. Either paper Higher3 marks

    The line \(L\) has equation \(6x + 7y + 2 = 0\)

    (a)

    Find the gradient of \(L\).

    (b)

    State the gradient of a line perpendicular to \(L\).

    Show answer
    (a) \(-\frac{6}{7}\)
    (b) \(\frac{7}{6}\)
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  10. Either paper Higher2 marks

    The line \(y = 2x + 1\) is perpendicular to the line \(y = ax - 1\).

    Calculate the value of \(a\).

    Show answer
    \(-\frac{1}{ 2 }\)
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discia.org Parallel and Perpendicular Lines · sheet 1
Answers Parallel and Perpendicular Lines · sheet 1
  1. (a) Line A and line C
    (b) Points at \((0, 5)\), \((1, 4)\), \((2, 3)\) and \((3, 2)\)
    (b)xy-2-1123123450
  2. \(y = -\frac{1}{3}x + k\) for any number \(k\) other than \(1\), for example \(y = -\frac{1}{3}x - 1\)
  3. (a) \(-\frac{1}{4}\)
    (b) \(-\frac{3}{2}\)
  4. (a) \(y = -3x + 6\) (any line \(y = -3x + k\) with \(k \neq -6\))
    (b) \(y = 3x + 7\)
  5. Parallel
  6. Yes
  7. Yes: the first line has gradient \(\frac{7}{3}\) and the second line has gradient \(\frac{7}{3}\)
  8. \(y = -\frac{1}{2}x - 2\)
  9. (a) \(-\frac{6}{7}\)
    (b) \(\frac{7}{6}\)
  10. \(-\frac{1}{ 2 }\)
discia.org Parallel and Perpendicular Lines · sheet 1