**Perpendicular** lines exist at right angles to each other.

Lines are perpendicular if the gradients of the two lines multiplied together = -1.

What is the equation of the line that is perpendicular to `y = 3x -3` and also passes through (0, 5)?

The gradient of the original line is 3. The gradient of the perpendicular line = - `frac(1)(3)` (reciprocal of the original gradient multiplied by -1).

The line passes through (0, 5), which is the intercept value, `c`.

Answer: y = -`frac(1)(3)`*x* + 5

Find the equation of the line perpendicular to `y = frac(1)(2)x - 3` that passes through (4, 4).

The gradient of the second line is given by - 1 / `frac(1)(2)` = -2

The lines passes through the point (4, 4): 4 = -2 x 4 + `c`, where c is the intercept = 12

The equation of the line is `y = -2x + 12`

Answer: `y = -2x + 12`

Check out our iOS app: tons of questions to help you practice for your GCSE maths. Download free on the App Store (in-app purchases required).