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4MA1/2FR Jan 2022, Question 24: Graphing a Single Inequality

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 5 marks

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The question, in short

Find the equation of a line with gradient −3 through (0, 5), then shade and label region R satisfying x ≤ 6, y ≥ 2 and y ≤ x + 1 on a grid.

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

Part (a) · 2 marks

Write the equation of the straight line having gradient −3 that passes through the point (0, 5).

  1. 1Gradient is −3, point (0, 5)
  2. 2Use y = mx + c
  3. 3m = −3, c = 5 because line passes through (0, 5)
  4. 4So y = −3x + 5

Answery = −3x + 5

Part (b) · 3 marks

On the grid, shade and label R, the region where x ≤ 6, y ≥ 2 and y ≤ x + 1 all hold.

  1. 1Draw vertical line at x = 6
  2. 2Draw horizontal line at y = 2
  3. 3Draw line y = x + 1 from x = 1 to x = 6
  4. 4Identify region where x ≤ 6 (left of x=6)
  5. 5y ≥ 2 (above y=2)
  6. 6y ≤ x + 1 (below the line y = x + 1)
  7. 7Shade the common region
  8. 8Label shaded region R

AnswerRegion R is the region satisfying x ≤ 6, y ≥ 2, and y ≤ x + 1, shown by shading on the grid

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