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Straight-line graphs: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on A9 Straight-line graphs, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q2

    June 2025 · Paper 2H

    2 marksA9 Straight-line graphsA10 Gradients and intercepts
    The whole paper ↗
    June 2025 Paper 2H, question 2: Here are lines A and B. Complete these statements. The equation of line A is The gradient of line B is

  2. Q11

    June 2025 · Paper 3H

    2 marksA9 Straight-line graphs
    The whole paper ↗
    June 2025 Paper 3H, question 11: (a) Write down the equation of a straight line parallel to y – 2x = 9 Answer 11 (b) A straight line • has gradient 5 • passes through the point (3, 7) Circle th

  3. Q17

    November 2024 · Paper 1H

    6 marksA16 Equation of a circle and tangentsA9 Straight-line graphs
    The whole paper ↗
    November 2024 Paper 1H, question 17: (a) A circle has centre (0, 0) and circumference 36π Work out the equation of the circle. Answer 17 (b) Point J has coordinates (15, 0) and point K has coordina

  4. Q17

    November 2024 · Paper 2H

    2 marksA9 Straight-line graphs
    The whole paper ↗
    November 2024 Paper 2H, question 17: Straight line LM has equation y = 4x – 7 Straight line ST has equation y = x − 9 4 Are the lines LM and ST perpendicular? Tick a box. Yes No Give a reason for y

  5. Q8

    November 2024 · Paper 3H

    4 marksG11 Geometry on coordinate axesA9 Straight-line graphs
    The whole paper ↗
    November 2024 Paper 3H, question 8: A triangle is drawn using the lines y = x x = –2 y = 4 Work out the coordinates of the three vertices of the triangle. Answer ( , ) ( , ) ( , )

  6. Q5

    June 2024 · Paper 2H

    4 marksA11 Quadratic graphs and turning pointsA9 Straight-line graphs
    The whole paper ↗
    June 2024 Paper 2H, question 5: (a) Here is a sketch of the graph y = –2x + 6 Complete the coordinates of C and D. C ( 0 , ) D ( , 0 ) 5 (b) Here is a sketch of a quadratic graph. Complete the

  7. Q7

    June 2024 · Paper 3H

    3 marksA9 Straight-line graphs
    The whole paper ↗
    June 2024 Paper 3H, question 7: Draw the graph of y = 1 – 2 1 x for values of x from –2 to 4

  8. Q15

    June 2024 · Paper 3H

    7 marksG11 Geometry on coordinate axesA9 Straight-line graphs
    The whole paper ↗
    June 2024 Paper 3H, question 15: A straight line passes through points A (–5, 9), B and C (3, –7). Not drawn accurately 15 (a) AB : BC = 1 : 3 Work out the coordinates of point B. Answer ( , )

  9. Q24

    November 2023 · Paper 1H

    1 markA9 Straight-line graphs
    The whole paper ↗
    November 2023 Paper 1H, question 24: Line A is perpendicular to line B. The gradient of line A is –2 Work out the gradient of line B. Answer

  10. Q13

    November 2023 · Paper 2H

    3 marksA9 Straight-line graphs
    The whole paper ↗
    November 2023 Paper 2H, question 13: A straight line passes through (3, 14) and (12, 32) Work out the equation of the line. Give your answer in the form y = mx + c Answer

  11. Q24

    June 2023 · Paper 1H

    5 marksG11 Geometry on coordinate axesA9 Straight-line graphs
    The whole paper ↗
    June 2023 Paper 1H, question 24: Points P, Q and R (8, 22) form a triangle. PQ is a horizontal line, with P on the y-axis. Angle PRQ is a right angle. The gradient of PR is 2 Work out the coord

  12. Q16

    June 2023 · Paper 2H

    3 marksA9 Straight-line graphs
    The whole paper ↗
    June 2023 Paper 2H, question 16: Line A has equation y = ax – 1 passes through the point (7, 13) Line B has equation 5y – 3x = 4 Show that line A has a greater gradient than line B.

  13. Q14

    November 2022 · Paper 1H

    2 marksA9 Straight-line graphs
    The whole paper ↗
    November 2022 Paper 1H, question 14: Craig wants to draw a graph, for values of x from –3 to 3, where the x-coordinate and y-coordinate are always in the ratio 2 : 1 Here is his graph. Make two cri

  14. Q1

    June 2022 · Paper 1H

    1 markA9 Straight-line graphs
    The whole paper ↗
    June 2022 Paper 1H, question 1: Which of these is the equation of a straight line? Circle your answer. y = 6x2 y = x – 6 y = x2 + 6 y = x 6

  15. Q24

    June 2022 · Paper 2H

    4 marksA9 Straight-line graphs
    The whole paper ↗
    June 2022 Paper 2H, question 24: A straight line is perpendicular to the straight line through (2, 8) and (6, 15) and passes through (0, 9) and (x, 17) Work out the value of x. x =

  16. Q13

    November 2021 · Paper 2H

    3 marksA9 Straight-line graphs
    The whole paper ↗
    November 2021 Paper 2H, question 13: A straight line has gradient 6 and passes through the point (3, 19) Work out the equation of the line. Give your answer in the form y = mx + c Answer

  17. Q16

    November 2021 · Paper 3H

    3 marksA9 Straight-line graphs
    The whole paper ↗
    November 2021 Paper 3H, question 16: P is the point (2, 14) Q is the point (6, 8) R is the point (2, 5) Use gradients to show that angle PQR is not a right angle.

  18. Q17

    November 2020 · Paper 1H

    3 marksA9 Straight-line graphs
    The whole paper ↗
    November 2020 Paper 1H, question 17: Jim buys a plant of height 20 cm The graph shows how the height of the plant changes during the next 4 days. Work out a formula for h in terms of n. Answer

  19. Q12

    November 2020 · Paper 2H

    2 marksA9 Straight-line graphs
    The whole paper ↗
    November 2020 Paper 2H, question 12: Work out the gradient of the straight line through (–2, 3) and (1, 9) Answer

  20. Q2

    November 2020 · Paper 3H

    1 markA9 Straight-line graphs
    The whole paper ↗
    November 2020 Paper 3H, question 2: Circle the equation of the line that is parallel to y = 2 1 x + 3 y = –2x y = 2x y = 2 1 x y = – 2 1 x
All 33 questions on Straight-line graphs, as a list
  1. June 2025, Paper 2H, Q2 (2 marks): Here are lines A and B. Complete these statements. The equation of line A is The gradient of line B is
  2. June 2025, Paper 3H, Q11 (2 marks): (a) Write down the equation of a straight line parallel to y – 2x = 9 Answer 11 (b) A straight line • has gradient 5 • passes through the point (3, 7) Circle th
  3. November 2024, Paper 1H, Q17 (6 marks): (a) A circle has centre (0, 0) and circumference 36π Work out the equation of the circle. Answer 17 (b) Point J has coordinates (15, 0) and point K has coordina
  4. November 2024, Paper 2H, Q17 (2 marks): Straight line LM has equation y = 4x – 7 Straight line ST has equation y = x − 9 4 Are the lines LM and ST perpendicular? Tick a box. Yes No Give a reason for y
  5. November 2024, Paper 3H, Q8 (4 marks): A triangle is drawn using the lines y = x x = –2 y = 4 Work out the coordinates of the three vertices of the triangle. Answer ( , ) ( , ) ( , )
  6. June 2024, Paper 2H, Q5 (4 marks): (a) Here is a sketch of the graph y = –2x + 6 Complete the coordinates of C and D. C ( 0 , ) D ( , 0 ) 5 (b) Here is a sketch of a quadratic graph. Complete the
  7. June 2024, Paper 3H, Q7 (3 marks): Draw the graph of y = 1 – 2 1 x for values of x from –2 to 4
  8. June 2024, Paper 3H, Q15 (7 marks): A straight line passes through points A (–5, 9), B and C (3, –7). Not drawn accurately 15 (a) AB : BC = 1 : 3 Work out the coordinates of point B. Answer ( , )
  9. November 2023, Paper 1H, Q24 (1 mark): Line A is perpendicular to line B. The gradient of line A is –2 Work out the gradient of line B. Answer
  10. November 2023, Paper 2H, Q13 (3 marks): A straight line passes through (3, 14) and (12, 32) Work out the equation of the line. Give your answer in the form y = mx + c Answer
  11. June 2023, Paper 1H, Q24 (5 marks): Points P, Q and R (8, 22) form a triangle. PQ is a horizontal line, with P on the y-axis. Angle PRQ is a right angle. The gradient of PR is 2 Work out the coord
  12. June 2023, Paper 2H, Q16 (3 marks): Line A has equation y = ax – 1 passes through the point (7, 13) Line B has equation 5y – 3x = 4 Show that line A has a greater gradient than line B.
  13. November 2022, Paper 1H, Q14 (2 marks): Craig wants to draw a graph, for values of x from –3 to 3, where the x-coordinate and y-coordinate are always in the ratio 2 : 1 Here is his graph. Make two cri
  14. June 2022, Paper 1H, Q1 (1 mark): Which of these is the equation of a straight line? Circle your answer. y = 6x2 y = x – 6 y = x2 + 6 y = x 6
  15. June 2022, Paper 2H, Q24 (4 marks): A straight line is perpendicular to the straight line through (2, 8) and (6, 15) and passes through (0, 9) and (x, 17) Work out the value of x. x =
  16. November 2021, Paper 2H, Q13 (3 marks): A straight line has gradient 6 and passes through the point (3, 19) Work out the equation of the line. Give your answer in the form y = mx + c Answer
  17. November 2021, Paper 3H, Q16 (3 marks): P is the point (2, 14) Q is the point (6, 8) R is the point (2, 5) Use gradients to show that angle PQR is not a right angle.
  18. November 2020, Paper 1H, Q17 (3 marks): Jim buys a plant of height 20 cm The graph shows how the height of the plant changes during the next 4 days. Work out a formula for h in terms of n. Answer
  19. November 2020, Paper 2H, Q12 (2 marks): Work out the gradient of the straight line through (–2, 3) and (1, 9) Answer
  20. November 2020, Paper 3H, Q2 (1 mark): Circle the equation of the line that is parallel to y = 2 1 x + 3 y = –2x y = 2x y = 2 1 x y = – 2 1 x
  21. November 2020, Paper 3H, Q28 (4 marks): Line A has equation y = 4x – 1 Line B is perpendicular to line A and passes through the point (8, 5) Work out the coordinates of the point where line B intersec
  22. November 2019, Paper 1H, Q22 (3 marks): (–3, 10) is a point on line L. (4, 0) and (6, 10) are points on line M. L and M are parallel. Work out the equation of line L. Give your answer in the form y =
  23. June 2019, Paper 1H, Q25 (6 marks): P (4, 8) is a point on a circle, centre O. The tangent at P intersects the axes at points A and B. Not drawn accurately 25 (a) Show that the gradient of the tan
  24. June 2019, Paper 2H, Q15 (4 marks): Here is line L and the graph of y = x – 1 The scales of the axes are not shown. Work out the equation of line L. Answer
  25. June 2019, Paper 3H, Q12 (3 marks): A straight line has gradient 4 and passes through the point (5, 23) Work out the equation of the line. Give your answer in the form y = mx + c Answer
  26. June 2018, Paper 3H, Q8 (5 marks): (a) Show that the lines y = 3x + 7 and 2y – 6x = 8 are parallel. Do not use a graphical method. 8 (b) Is the point (–5, –6) above, below or on the line y = 3x +
  27. June 2018, Paper 3H, Q16 (1 mark): Two straight lines intersect at point A. Circle the coordinates of A. (– 4 3 , 3) (–4, 3) (–12, 3) (– 3 4 , 3) Not drawn accurately
  28. November 2017, Paper 2H, Q13 (1 mark): Two straight lines intersect at point P. Circle the coordinates of P. (–3, –1)       − − 3 1 1, (–1, –3)       − − 1 , 3 1 Not drawn accurately
  29. November 2017, Paper 3H, Q4 (1 mark): Circle the equation of the line that is parallel to the x-axis. y = –5 x – y = 0 x = 3 x + y = 0
  30. June 2017, Paper 1H, Q17 (4 marks): A is the point (2, –5) B is the point (4, –9) 17 (a) Show that the gradient of the straight line passing through A and B is –2 17 (b) C is the point (–301, 601)
  31. June 2017, Paper 1H, Q27 (4 marks): P (–1, 4) is a point on a circle, centre O Not drawn accurately Work out the equation of the tangent to the circle at P. Give your answer in the form y = mx + c
  32. June 2017, Paper 2H, Q14 (3 marks): The graph shows the cost of some taxi journeys. Work out a formula for C in terms of n. Answer
  33. Specimen, Paper 2H, Q4 (1 mark): Circle the equation of a line that is parallel to y = 5x – 2 y = 2x – 5 y = 5x + 2 y = 3x – 2 y = – 5 1 x – 2

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