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4024/12 May/Jun 2026, Question 15: Straight-line equations

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 8 marks

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The question, in short

Line L is 2y + x = 19. Find its gradient and y-intercept, show that the line perpendicular to L through (−1, −5) is y = 2x − 3, and find where the two lines meet.

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

Part (ai) · 2 marks

  1. 12y = 19 − x
  2. 2y = −1/2 x + 19/2
  3. 3Gradient = −1/2

Answer−1/2

Part (aii) · 1 mark

  1. 1y = −1/2 x + 19/2
  2. 2y-intercept = 19/2

Answer19/2

Part (b) · 2 marks

Show the perpendicular line through (−1, −5) is y = 2x − 3.

  1. 1Perpendicular gradient: m × (−1/2) = −1, so m = 2
  2. 2y = 2x + c through (−1, −5): −5 = 2 × (−1) + c
  3. 3c = −3
  4. 4y = 2x − 3

AnswerGradient of M = 2 since −1/2 × 2 = −1; −5 = 2 × (−1) + c gives c = −3, so y = 2x − 3

Part (c) · 3 marks

Point where 2y + x = 19 and y = 2x − 3 meet.

  1. 12(2x − 3) + x = 19
  2. 25x − 6 = 19
  3. 3x = 5
  4. 4y = 2 × 5 − 3 = 7

Answer(5, 7)

Stuck on a step? Read the free lesson: Solving by Substitution

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Also searched as: 4024/12/M/J/26 · 4024_s26_qp_12 · 4024 s26 12 · question 15.
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