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4PM1/02 Jun 2023, Question 5: Drawing Straight-Line Graphs

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks

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The question, in short

Draw three straight lines on a coordinate grid, shade the region satisfying three inequalities, then use the graph to find the minimum of P = 2x − 5y.

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

Part (a) · 3 marks

Plot the lines y = 2x + 5, 4y = x − 8 and 5y + 3x = 30 on the grid.

  1. 1y = 2x + 5: plot (0, 5) and (−2.5, 0)
  2. 24y = x − 8: plot (0, −2) and (8, 0)
  3. 35y + 3x = 30: plot (0, 6) and (10, 0)

Answery = 2x + 5 through (−2.5, 0) and (0, 5); 4y = x − 8 through (0, −2) and (8, 0); 5y + 3x = 30 through (0, 6) and (10, 0)

Part (b) · 1 mark

Shade the region R meeting y ≤ 2x + 5, 4y ≥ x − 8 and 5y + 3x ≤ 30.

  1. 1R lies below y = 2x + 5, above 4y = x − 8 and below 5y + 3x = 30
  2. 2It is the triangle enclosed by the three lines

AnswerR is the triangle with vertices about (−4, −3), (9.4, 0.4) and (0.4, 5.8): below y = 2x + 5, above 4y = x − 8 and below 5y + 3x = 30

Part (c) · 3 marks

Use the shaded region to work out the smallest value of P = 2x − 5y.

  1. 1Vertices of R from the graph: (9.4, 0.4), (−4, −3), (0.4, 5.8)
  2. 2P at (9.4, 0.4) = 16.8; at (−4, −3) = 7; at (0.4, 5.8) = −28.2
  3. 3Least value of P = −28.2

Answer−28.9 to −27.5

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