GCSE · Straight-line graphs

Parallel and perpendicular linesExam-style questions

Why parallel lines share a gradient (and nothing else), why perpendicular gradients multiply to −1 (the negative reciprocal), and how to build a line through a given point with either condition.

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18 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Write down the equation of the straight line that is parallel to $y = 2x - 1$ and passes through the point $(0, 7)$
Level 4 · 2 marksTry it
2
The line $L$ has equation $y = 4x - 3$

Write down the gradient of a line perpendicular to $L$ .
Level 4 · 2 marksTry it
3
The line $L$ has equation $y = \tfrac{1}{2}x + 4$

(a) Write down the gradient of a line perpendicular to $L$ .

(b) Find the equation of the line perpendicular to $L$ that passes through the point $(2, 1)$
Level 4 · 3 marksTry it
4
Line $A$ has equation $y = 2x + 1$

Line $B$ has equation $2y = 4x - 3$

Are lines $A$ and $B$ parallel? You must show your working.
Level 4 · 2 marksTry it
5
The straight line $L_1$ has equation $3y = 12x - 5$

The straight line $L_2$ is perpendicular to $L_1$ and passes through the point $(8, 1)$ .

Find an equation of $L_2$ .

Give your answer in the form $ax + by + c = 0$ , where $a$ , $b$ and $c$ are integers. (4 marks)
Level 4 · 4 marksTry it

1 more question on parallel and perpendicular lines

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