[discia] GCSE Maths › Algebra › Equation of a Line

Equation of a Line

discia.org 10 questions · 30 marks
Name Date
  1. Either paper 2 marks

    A line has equation \(y = -3x + 9\)

    (a)

    Write down the coordinates of the point where the line intersects the \(y\)-axis.

    (b)

    Write down the coordinates of the point where the line intersects the \(x\)-axis.

    Show answer
    (a) \((0, 9)\)
    (b) \((3, 0)\)
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  2. Either paper 2 marks

    Determine whether the point \((-2, 2)\) lies on the line \(y = -3x - 4\).

    You must show your working.

    Show answer
    Yes
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  3. Either paper 3 marks

    The line \(L\) is drawn on the grid.

    -7-6-5-4-3-21234567-9-8-7-6-5-4-3-21234567890xy
    (a)

    Find the equation of \(L\).

    (b)

    The point \((-2, s)\) lies on \(L\).

    Calculate the value of \(s\).

    Show answer
    (a) \(y = x\)
    (b) \(-2\)
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  4. Either paper 3 marks

    The line \(L\) is drawn on the grid.

    -7-6-5-4-3-21234567-9-8-7-6-5-4-3-21234567890xy

    Find the equation of \(L\).

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

    Show answer
    \(y = x - 1\)
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  5. Either paper 4 marks

    The line \(L\) is drawn on the grid.

    -6-5-4-3-2123456-8-7-6-5-4-3-2123456780xy
    (a)

    Find the equation of \(L\), in the form \(y = mx + c\).

    (b)

    Another line is parallel to \(L\) and crosses the \(y\)-axis at \((0, -3)\).

    Write down the equation of that line.

    Show answer
    (a) \(y = x + 3\)
    (b) \(y = x - 3\)
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  6. Either paper 3 marks

    A straight line passes through \((-4, -7)\) and \((1, 8)\).

    Find the equation of the line.

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

    Show answer
    \(y = 3x + 5\)
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  7. Either paper 3 marks

    A straight line has gradient \(-3\) and passes through the point \((-5, 21)\).

    Work out the equation of the line.

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

    Show answer
    \(y = -3x + 6\)
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  8. Either paper 3 marks

    A straight line has equation \(4y = 16x - 24\)

    (a)

    Rearrange the equation into the form \(y = mx + c\).

    (b)

    State the gradient of the line.

    Show answer
    (a) \(y = 4x - 6\)
    (b) \(4\)
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  9. Either paper 3 marks

    A straight line has equation \(x + y = -5\)

    (a)

    Rearrange the equation into the form \(y = mx + c\).

    (b)

    State the gradient of the line.

    Show answer
    (a) \(y = -x - 5\)
    (b) \(-1\)
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  10. Either paper 4 marks

    \(A\) is the point \((3, -19)\).

    \(B\) is the point \((5, -27)\).

    (a)

    Show that the gradient of the straight line passing through \(A\) and \(B\) is \(-4\).

    (b)

    \(C\) is the point \((255, -1027)\).

    Does \(C\) lie on the straight line passing through \(A\) and \(B\)?

    You must show your working.

    Show answer
    (a) \(\frac{ -27 - (-19) }{ 5 - 3 } = \frac{ -8 }{ 2 } = -4\)
    (b) Yes: the line gives \(y = -1027\) at \(x = 255\), and \(C\) has \(y = -1027\)
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discia.org Equation of a Line · sheet 1
Answers Equation of a Line · sheet 1
  1. (a) \((0, 9)\)
    (b) \((3, 0)\)
  2. Yes
  3. (a) \(y = x\)
    (b) \(-2\)
  4. \(y = x - 1\)
  5. (a) \(y = x + 3\)
    (b) \(y = x - 3\)
  6. \(y = 3x + 5\)
  7. \(y = -3x + 6\)
  8. (a) \(y = 4x - 6\)
    (b) \(4\)
  9. (a) \(y = -x - 5\)
    (b) \(-1\)
  10. (a) \(\frac{ -27 - (-19) }{ 5 - 3 } = \frac{ -8 }{ 2 } = -4\)
    (b) Yes: the line gives \(y = -1027\) at \(x = 255\), and \(C\) has \(y = -1027\)
discia.org Equation of a Line · sheet 1