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0580/12 Feb/Mar 2025, Question 17: Finding the Equation From a Graph

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 4 marks

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The question, in short

A straight line L is drawn on a grid with axes 0 to 8 and 0 to 7. Find its equation in the form y = mx + c, then find where L meets the x-axis at P.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Using the grid, work out the gradient and y-intercept of line L and write its equation as y = mx + c.

  1. 1L crosses the y-axis at (0, 3), so c = 3
  2. 2L passes through (8, 7): gradient = (7 − 3)/(8 − 0) = 4/8 = 1/2
  3. 3y = 1/2 x + 3

Answery = 1/2 x + 3

Part (b) · 2 marks

Line L meets the x-axis at point P. Determine the coordinates of P.

  1. 1On the x-axis y = 0
  2. 20 = 1/2 x + 3
  3. 31/2 x = −3, so x = −6
  4. 4P = (−6, 0)

Answer(−6, 0)

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