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0580/31 May/Jun 2022, Question 8: Finding the Equation From a Graph

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 6 marks

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The question, in short

From a grid showing line L through (0, 2) and (4, 0), determine its equation, complete a table and draw y = 2x + 5, then find where the two lines meet and a parallel line through (0, 18).

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

Part (a) · 2 marks

Work out the equation of line L in the form y = mx + c.

  1. 1Gradient = rise ÷ run = −2 ÷ 4 = −1/2
  2. 2y-intercept = 2
  3. 3y = −(1/2)x + 2

Answery = −(1/2)x + 2

Part (bi) · 1 mark

Fill in the missing y-value in the table for y = 2x + 5 at x = −3.

  1. 1y = 2 × (−3) + 5 = −1

Answer−1

Part (bii) · 1 mark

Plot the graph of y = 2x + 5 on the grid.

  1. 1Plot (−5, −5), (−3, −1), (0, 5) and join with a ruled straight line

AnswerCorrect ruled line on grid

Part (c) · 1 mark

State the coordinates where line L and y = 2x + 5 intersect.

  1. 1−(1/2)x + 2 = 2x + 5, so −2.5x = 3, x = −1.2
  2. 2y = 2 × (−1.2) + 5 = 2.6
  3. 3(−1.2, 2.6)

Answer(−1.2, 2.6)

Part (d) · 1 mark

Give the equation of the line parallel to y = 2x + 5 passing through (0, 18).

  1. 1Parallel so gradient 2; passes through (0, 18) so c = 18
  2. 2y = 2x + 18

Answery = 2x + 18

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Also searched as: 0580/31/M/J/22 · 0580_s22_qp_31 · 0580 s22 31 · question 8.
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