Parallel lines have the same gradient.

All of these lines have a gradient of 5.

Perpendicular lines have gradients which multiply together to give -1.

Here one line has a gradient of 5 and the other of -1/5.

To find the gradient of a line which is **perpendicular** to one of gradient a/b, we invert the fraction and multiply by -1.

This means you don't need diagrams to check if lines are perpendicular.

**Example**

State the gradient of a line which is perpendicular to one of gradient ¾.

**Answer**

Invert the fraction and multiply by -1.

3 | → | 4 | → | -4 |

4 | 3 | 3 |

Answer is | -4 |

3 |