Graphs 5

4 marks · Normal

The line l has equation .

(a)

Write down the gradient of l.

[1 mark]

(b)

Find the gradient of a line perpendicular to l.

[1 mark]

(c)

Find the equation of a line perpendicular to l that passes through the point (2, 1), giving your answer in the form .

[2 marks]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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(a) 2

(b) -1/2

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Gradient of l given as 2

M1 (b) · 1 mark · Uses negative reciprocal, gives -1/2

M1 (c) · 1 mark · Carries method using perpendicular gradient and substitute point into y = mx + c (follow-through)

A1 (c) · 1 mark · Correct equation: y = -1/2 x + 2 (follow-through)

Worked solution

a) The gradient of l is 2.

b) The gradient of a perpendicular line is the negative reciprocal: .

c) Equation: y = -1/2 x + c. Substitute (2, 1):

So the equation is y = -1/2 x + 2.