0580/31 May/Jun 2021, Question 4: The Equation y = mx + c

Part (a) · 1 mark

State the coordinates of point A from the grid.

1. 1Read from the grid: A = (−2, 4)

Answer(−2, 4)

Part (bi) · 1 mark

Calculate the gradient of line L.

1. 1L passes through A(−2, 4) and B(6, 0)
2. 2Gradient = (0 − 4)/(6 − (−2)) = −4/8 = −0.5

Answer−0.5

Part (bii) · 2 marks

Give the equation of line L as y = mx + c.

1. 1Gradient m = −0.5 (down 1 for every 2 across).
2. 2L crosses the y-axis at (0, 3), so c = 3.
3. 3y = −0.5x + 3

Answer−0.5x + 3

Part (ci) · 1 mark

Draw a line through A perpendicular to line L.

1. 1Perpendicular gradient = −1 ÷ (−0.5) = 2
2. 2From A(−2, 4) go down 4 and left 2 to (−4, 0); draw a ruled line through A and (−4, 0).

AnswerCorrect ruled line drawn

Part (cii) · 1 mark

Mark where this perpendicular meets the x-axis as C and state its coordinates.

1. 1The line has gradient 2 through A(−2, 4): 0 = 4 + 2(x + 2), so x = −4
2. 2C = (−4, 0)

Answer(−4, 0)

Part (ciii) · 2 marks

Measure the side lengths and find the perimeter of triangle ABC.

1. 1BC = 6 − (−4) = 10 cm
2. 2AB = √(8² + 4²) = √80 ≈ 8.9 cm
3. 3AC = √(2² + 4²) = √20 ≈ 4.5 cm
4. 4Perimeter ≈ 10 + 8.9 + 4.5 = 23.4 cm

Answer23.0 to 23.8

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