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0580/22 Feb/Mar 2022, Question 16: The Equation y = mx + c

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

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The question, in short

Using points A(−6, 5) and B(−2, −3) on a grid, find the equation of line l through A and B, then the perpendicular line through the origin.

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Part (a) · 2 marks

Find the equation of the straight line through A(−6, 5) and B(−2, −3), giving it as y = mx + c.

  1. 1Gradient = (−3 − 5)/(−2 − (−6)) = −8/4 = −2
  2. 2y = −2x + c through (−6, 5): 5 = 12 + c, so c = −7
  3. 3y = −2x − 7

Answery = −2x − 7

Part (b) · 2 marks

Find the equation of the line perpendicular to l that passes through the origin.

  1. 1Perpendicular gradient = −1 ÷ (−2) = 1/2
  2. 2Through the origin, so c = 0
  3. 3y = (1/2)x

Answery = (1/2)x

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Also searched as: 0580/22/F/M/22 · 0580_m22_qp_22 · 0580 m22 22 · question 16.
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