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Parallel and Perpendicular Lines

discia.org 10 questions · 26 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.

    -2-1123123450xy

    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)-2-1123123450xy
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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 \(y = -\frac{1}{3}x - 1\)
    Another like this
  3. Either paper 2 marks
    (a)

    Write down the equation of a straight line that is parallel to \(y - 4x = -5\)

    (b)

    A straight line

    - has gradient \(-4\) - passes through the point \((-3, 6)\)

    Circle the equation of the line.

    \(y = -4x\)

    \(y = -3x - 3\)

    \(y = -4x + 6\)

    \(y = -4x - 6\)

    Show answer
    (a) \(y = 4x + 5\) (any line \(y = 4x + k\) with \(k \neq -5\))
    (b) \(y = -4x - 6\)
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  4. Either paper 2 marks

    Here are the equations of two straight lines.

    \(y = \frac{ 3 }{ 5 }x - 3\)

    \(15y = -9x + 5\)

    Isla says that the lines are parallel.

    Is Isla correct? You must give a reason for your answer.

    Show answer
    No: the first line has gradient \(\frac{3}{5}\) and the second line has gradient \(-\frac{3}{5}\)
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  5. Either paper 5 marks

    Do not use a graphical method in either part of this question.

    (a)

    Show that the lines \(y = 2x + 3\) and \(5y - 10x = 40\) are parallel.

    (b)

    Is the point \((-1, -2)\) above, below or on the line \(y = 2x + 3\)?

    Tick one box.

    Above    Below    On the line

    You must show your working.

    Show answer
    (a) \(5y - 10x = 40\) rearranges to \(y = 2x + 8\); both lines have gradient \(2\), so they are parallel
    (b) Below: the line has \(y = 1\) at \(x = -1\) and the point has \(y = -2\)
    Another like this
  6. 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.

    -1123456-2-1123450xy

    There are four points on this grid that each have both coordinates that are whole numbers and \(x\)-coordinate \(+\) \(y\)-coordinate \(= 8\)

    Plot the four points on the grid.

    Show answer
    (a) Line A and line B
    (b) Points at \((3, 5)\), \((4, 4)\), \((5, 3)\) and \((6, 2)\)
    (b)-1123456-2-1123450xy
    Another like this
  7. Either paper 1 mark

    Write down the equation of a line that is parallel to \(y = -\frac{5}{3}x + 6\)

    Show answer
    \(y = -\frac{5}{3}x + k\) for any number \(k\) other than \(6\), for example \(y = -\frac{5}{3}x - 6\)
    Another like this
  8. Either paper 2 marks
    (a)

    Write down the equation of a straight line that is parallel to \(y + 4x = -9\)

    (b)

    A straight line

    - has gradient \(-6\) - passes through the point \((-2, 4)\)

    Circle the equation of the line.

    \(y = 5x + 14\)

    \(y = -6x\)

    \(y = -6x + 4\)

    \(y = -6x - 8\)

    Show answer
    (a) \(y = -4x + 9\) (any line \(y = -4x + k\) with \(k \neq -9\))
    (b) \(y = -6x - 8\)
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  9. Either paper 2 marks

    Here are the equations of two straight lines.

    \(y = \frac{ 4 }{ 3 }x + 2\)

    \(12y = 9x + 2\)

    Amara says that these lines are parallel.

    Is Amara correct?

    You must give a reason for your answer.

    Show answer
    No: the first line has gradient \(\frac{4}{3}\) and the second line has gradient \(\frac{3}{4}\)
    Another like this
  10. Either paper 5 marks

    Do not use a graphical method in either part of this question.

    (a)

    Show that the lines \(y = 3x + 7\) and \(5y - 15x = 25\) are parallel.

    (b)

    Is the point \((-3, 2)\) above, below or on the line \(y = 3x + 7\)?

    Tick one box.

    Above    Below    On the line

    You must show your working.

    Show answer
    (a) \(5y - 15x = 25\) rearranges to \(y = 3x + 5\); both lines have gradient \(3\), so they are parallel
    (b) Above: the line has \(y = -2\) at \(x = -3\) and the point has \(y = 2\)
    Another like this
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)-2-1123123450xy
  2. \(y = -\frac{1}{3}x + k\) for any number \(k\) other than \(1\), for example \(y = -\frac{1}{3}x - 1\)
  3. (a) \(y = 4x + 5\) (any line \(y = 4x + k\) with \(k \neq -5\))
    (b) \(y = -4x - 6\)
  4. No: the first line has gradient \(\frac{3}{5}\) and the second line has gradient \(-\frac{3}{5}\)
  5. (a) \(5y - 10x = 40\) rearranges to \(y = 2x + 8\); both lines have gradient \(2\), so they are parallel
    (b) Below: the line has \(y = 1\) at \(x = -1\) and the point has \(y = -2\)
  6. (a) Line A and line B
    (b) Points at \((3, 5)\), \((4, 4)\), \((5, 3)\) and \((6, 2)\)
    (b)-1123456-2-1123450xy
  7. \(y = -\frac{5}{3}x + k\) for any number \(k\) other than \(6\), for example \(y = -\frac{5}{3}x - 6\)
  8. (a) \(y = -4x + 9\) (any line \(y = -4x + k\) with \(k \neq -9\))
    (b) \(y = -6x - 8\)
  9. No: the first line has gradient \(\frac{4}{3}\) and the second line has gradient \(\frac{3}{4}\)
  10. (a) \(5y - 15x = 25\) rearranges to \(y = 3x + 5\); both lines have gradient \(3\), so they are parallel
    (b) Above: the line has \(y = -2\) at \(x = -3\) and the point has \(y = 2\)
discia.org Parallel and Perpendicular Lines · sheet 1