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4PM1/02R Jan 2020, Question 2: Equation of a Line Through Two Points

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks

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The question, in short

From a diagram of two lines and shaded region R, find integer-form equations for l₁ and l₂, then state three inequalities defining R.

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

Part (a) · 3 marks

Find equations of l₁ and l₂ in the form ax + by = c with integer coefficients, using the given intercept points.

  1. 1l₁: gradient = (0 − 8)/(4 − 0) = −2, y = −2x + 8, so 2x + y = 8
  2. 2l₂: gradient = (0 − 4)/(6 − 0) = −2/3, y = −(2/3)x + 4
  3. 33y = −2x + 12, so 2x + 3y = 12

Answerl₁: 2x + y = 8; l₂: 2x + 3y = 12

Part (b) · 3 marks

Using your line equations, write three inequalities whose solution region is R.

  1. 1R is to the right of the y-axis: x ≥ 0
  2. 2R is below l₁ (same side as O): 2x + y ≤ 8
  3. 3R is above l₂ (opposite side from O): 2x + 3y ≥ 12

Answerx ≥ 0, 2x + y ≤ 8, 2x + 3y ≥ 12 (strict inequalities also accepted)

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