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Exam questions · Maths · Graphs

Straight-Line Graphs

  • 6 exam questions
  • 18 marks
  • 9 quick checks
  1. 1 Calculate [2 marks]

    Calculate the gradient of the line through \((1, 2)\) and \((5, 10)\).

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    Model answer

    \(\dfrac{10 - 2}{5 - 1} = \dfrac{8}{4} = 2\).

    Mark scheme

    • \(\dfrac{10 - 2}{5 - 1}\) — M1
    • 2 — A1
  2. 2 Complete [3 marks]

    (a) Complete the table of values for \(y = 4x - 3\). \(x = 0, 1, 2, 3\) [2 marks] (b) Write down the \(y\)-intercept of the line \(y = 4x - 3\). [1 mark]

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    Model answer

    (a) The values are \(-3, 1, 5, 9\). (b) The \(y\)-intercept is \(-3\), where \(x = 0\).

    Mark scheme

    • (a) At least two correct values — M1
    • (a) \(-3, 1, 5, 9\) — A1
    • (b) \(-3\) — B1
  3. 3 Calculate [4 marks]

    The diagram shows a straight line passing through the points \(P\) and \(Q\). (a) Calculate the gradient of the line. [2 marks] (b) Write down the equation of the line. [2 marks]

    A steep straight line through the points P (1, 1) and Q (3, 7), crossing the y-axis at minus 2.
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    Model answer

    (a) \(\dfrac{7 - 1}{3 - 1} = \dfrac{6}{2} = 3\). (b) The line crosses the \(y\)-axis at \(-2\), so \(y = 3x - 2\).

    Mark scheme

    • (a) \(\dfrac{7 - 1}{3 - 1}\) — M1
    • (a) 3 — A1
    • (b) \(y = 3x + c\) or \(y = mx - 2\) — M1
    • (b) \(y = 3x - 2\) — A1
  4. 4 Find [2 marks]

    Find the equation of the line that is parallel to \(y = 3x - 7\) and passes through the point \((0, 2)\).

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    Model answer

    The gradient is 3 and the \(y\)-intercept is 2, so \(y = 3x + 2\).

    Mark scheme

    • Gradient 3 or \(c = 2\) used — M1
    • \(y = 3x + 2\) — A1
  5. 5 Find [3 marks]

    A straight line has gradient \(-2\) and passes through the point \((0, 5)\). (a) Write down the equation of the line. [1 mark] (b) Does the point \((4, -3)\) lie on the line? Show how you know. [2 marks]

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    Model answer

    (a) \(y = -2x + 5\). (b) When \(x = 4\), \(y = -2 \times 4 + 5 = -3\), so the point lies on the line.

    Mark scheme

    • (a) \(y = -2x + 5\) — B1
    • (b) \(-2 \times 4 + 5\) or \(-8 + 5\) — M1
    • (b) \(-3\) with a conclusion — A1
  6. 6 Show that [4 marks]

    \(A\) is the point \((-3, 2)\) and \(B\) is the point \((5, 6)\). (a) Work out the gradient of \(AB\). [2 marks] (b) Show that the line \(y = \dfrac{1}{2}x + 3.5\) passes through \(A\). [2 marks]

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    Model answer

    (a) \(\dfrac{6 - 2}{5 - (-3)} = \dfrac{4}{8} = \dfrac{1}{2}\). (b) When \(x = -3\), \(y = \dfrac{1}{2} \times (-3) + 3.5 = -1.5 + 3.5 = 2\), so the line passes through \(A\).

    Mark scheme

    • (a) \(\dfrac{6 - 2}{5 - (-3)}\) — M1
    • (a) \(\dfrac{1}{2}\) — A1
    • (b) \(\dfrac{1}{2} \times (-3) + 3.5\) — M1
    • (b) 2 with a conclusion — A1

Quick check

  1. 1

    What is the equation of the \(x\)-axis?

    1. A\(x = 0\)
    2. B\(y = 0\)
    3. C\(y = x\)
    4. D\(x + y = 0\)
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    B: \(y = 0\)

    Every point on the \(x\)-axis has \(y = 0\).

  2. 2

    Which point is on the line \(y = 3x - 2\)?

    1. A\((4, 10)\)
    2. B\((2, 6)\)
    3. C\((1, 3)\)
    4. D\((0, 2)\)
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    A: \((4, 10)\)

    Put in the coordinates: \(3 \times 4 - 2 = 10\), so \((4, 10)\) fits.

  3. 3

    Work out the gradient of the line through \((1, 7)\) and \((4, 1)\).

    1. A\(2\)
    2. B\(-\dfrac{1}{2}\)
    3. C\(-6\)
    4. D\(-2\)
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    D: \(-2\)

    \(\dfrac{1 - 7}{4 - 1} = \dfrac{-6}{3} = -2\).

  4. 4

    Which line is parallel to \(y = 3x + 1\)?

    1. A\(y = x + 3\)
    2. B\(y = -3x + 1\)
    3. C\(y = 3x - 5\)
    4. D\(y = \dfrac{1}{3}x + 1\)
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    C: \(y = 3x - 5\)

    Parallel lines have the same gradient, 3.

  5. 5

    What is the equation of the vertical line through 4 on the \(x\)-axis?

    1. A\(y = 4\)
    2. B\(x = 4\)
    3. C\(x + y = 4\)
    4. D\(y = x\)
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    B: \(x = 4\)

    Every point on the line has \(x = 4\).

  6. 6

    What is the gradient of the line \(y = 5 - 3x\)?

    1. A\(-3\)
    2. B\(5\)
    3. C\(3\)
    4. D\(-5\)
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    A: \(-3\)

    Written as \(y = -3x + 5\), the number multiplying \(x\) is \(-3\).

  7. 7

    What is the value of \(y\) on the line \(y = 2x - 1\) when \(x = -1\)?

    1. A\(-1\)
    2. B\(1\)
    3. C\(-2\)
    4. D\(-3\)
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    D: \(-3\)

    \(2 \times (-1) - 1 = -2 - 1 = -3\).

  8. 8

    Where does the line \(y = 3x + 2\) cross the \(y\)-axis?

    1. A\((2, 0)\)
    2. B\((0, 3)\)
    3. C\((0, 2)\)
    4. D\((0, -2)\)
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    C: \((0, 2)\)

    The number on its own, 2, is the \(y\)-intercept.

  9. 9

    Work out the gradient of the line through \((-2, 3)\) and \((4, -9)\).

    1. A\(2\)
    2. B\(-2\)
    3. C\(-\dfrac{1}{2}\)
    4. D\(-6\)
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    B: \(-2\)

    \(\dfrac{-9 - 3}{4 - (-2)} = \dfrac{-12}{6} = -2\).