# Parallel and perpendicular lines

Parallel lines never meet and have the same gradient. Perpendicular lines meet at a right angle and their gradients multiply to give -1.

Maths (school) · Part 04: Graphs · Card 4 of 8 · Last updated 2026-10-19

## Analogy

Parallel lines are like railway tracks. Perpendicular lines are like a crossroads.

## Example

**Starting with y = 2x + 1**

Parallel: y = 2x - 5
Perpendicular gradient: -1/2
Because 2 x (-1/2) = -1

## In practice

City street grids use parallel roads crossed by perpendicular ones.

## Practice

### Flashcards

- **What is the gradient of a line perpendicular to a line with gradient 2?** -1/2. The two gradients multiply to -1.

## Questions people ask

### How do you find a perpendicular gradient?

Flip the fraction upside down and change the sign. A gradient of 2, which is 2/1, becomes -1/2. A gradient of -3/4 becomes 4/3. You can check by multiplying the two gradients together, which must always give -1. Perpendicular lines meet at a right angle.

### Why do parallel lines have the same gradient?

The gradient measures steepness. Two lines with the same steepness rise at the same rate, so they stay the same distance apart and never meet. If the gradients differ, one line gets closer to the other and they must cross somewhere.

## Related concepts

- [Gradient](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-2)
- [y = mx + c](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-3)
- [Midpoint of a line](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-5)
- [Coordinates](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-1)

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