Graphs 1

3 marks · Hard

Consider the line y = 4x – 7.

(a)

Explain whether the point (2, 2) lies above, below, or on the line.

[2 marks]

(b)

Give a reason for your answer.

[1 mark]

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(a) Below the line

(b) Substituting x = 2: y = 4×2 – 7 = 1. The point has y = 2, which is greater than 1. So it lies above.

Common mistakes: Incorrect substitution; Misinterpreting above vs. below

Show mark scheme and worked solution

Marking points

B1 (a) · 2 marks · Identifies correctly that (2, 2) is above the line y = 4x – 7.

B2 (b) · 1 mark · Provides correct calculation and explanation reasoning (substituting x = 2: y = 1 on the line, but point is y = 2, so above).

Worked solution

a) For x = 2, y on line = 4×2 – 7 = 8 – 7 = 1.

Point (2, 2) has y-coordinate 2, which is greater than the y for the line (which is 1).

So (2, 2) lies above the line.

b) This is because y = 2 > 1 for x = 2.