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0580/32 Oct/Nov 2025, Question 25: The Equation y = mx + c

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 5 marks

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The question, in short

From a grid showing line L, determine its equation as y = mx + c, then find a line parallel to y = −3x + 5 passing through (1, 5).

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Part (a) · 3 marks

Work out the gradient and intercept of line L from the grid, then state its equation as y = mx + c.

  1. 1L crosses the y-axis at (0, 2), so c = 2
  2. 2From (0, 2) to (8, 4): rise = 2, run = 8
  3. 3m = 2 ÷ 8 = 1/4
  4. 4y = (1/4)x + 2

Answer(1/4)x + 2

Part (b) · 2 marks

Using the gradient of y = −3x + 5, write the equation of the parallel line through (1, 5) as y = mx + c.

  1. 1Parallel lines have equal gradients, so m = −3
  2. 25 = −3 × 1 + c, so c = 8
  3. 3y = −3x + 8

Answer−3x + 8

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Also searched as: 0580/32/O/N/25 · 0580_w25_qp_32 · 0580 w25 32 · question 25.
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