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
Find the equation of the straight line that is perpendicular to $y = 2x + 3$ and passes through the point $(4, 1)$
Level 5 · 3 marksTry it
2
Show that the lines $y = 3x - 2$ and $x + 3y = 6$ are perpendicular.
Level 5 · 3 marksTry it
3
The line $L_1$ has equation $y = 5 - 2x$

The line $L_2$ is parallel to $L_1$ and passes through the point $(3, 4)$ .

Find the coordinates of the point where $L_2$ crosses the $y$ -axis.
Level 5 · 3 marksTry it
4
Find the equation of the straight line that is perpendicular to $3x + y = 7$ and passes through the point $(3, 2)$
Level 5 · 3 marksTry it
5
The line $L_1$ has equation $y = 4x - 1$

The line $L_2$ is perpendicular to $L_1$ and passes through the point $(8, 0)$ .

Find the coordinates of the point where $L_2$ crosses the $y$ -axis.
Level 5 · 3 marksTry it