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0580/22 May/Jun 2026, Question 12: Drawing Straight-Line Graphs

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 7 marks

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The question, in short

On a grid from 0 to 9 on both axes, draw four given straight lines, then use shading to identify and label the region R satisfying four inequalities.

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

Part (a) · 5 marks

Draw the four straight lines x = 8, y = 2, x + y = 8 and 2y − x = 4 on the grid.

  1. 1x = 8: vertical line through (8, 0); y = 2: horizontal line through (0, 2)
  2. 2x + y = 8: through (0, 8) and (8, 0)
  3. 32y − x = 4: through (0, 2) and (8, 6)
  4. 4Draw all four as solid ruled lines

AnswerFour ruled solid straight lines: x = 8, y = 2, x + y = 8, 2y − x = 4

Part (b) · 2 marks

Shade the unwanted regions of the grid to find and label the region R defined by the four inequalities.

  1. 1Shade to the right of x = 8 and below y = 2
  2. 2Shade below x + y = 8 and above 2y − x = 4
  3. 3The unshaded region with vertices (6, 2), (8, 2), (8, 6), (4, 4) is R; label it R

AnswerCorrect region R identified: the quadrilateral with vertices (6, 2), (8, 2), (8, 6), (4, 4)

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Also searched as: 0580/22/M/J/26 · 0580_s26_qp_22 · 0580 s26 22 · question 12.
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