# Gradient

How steep a line is. It is the amount the line goes up for every 1 step across.

Maths (school) · Part 04: Graphs · Card 2 of 8 · Last updated 2026-10-19

## Analogy

Like the slope of a hill: a bigger number means a harder climb.

## Example

**Points (1, 2) and (5, 10)**

Up = 10 - 2 = 8
Across = 5 - 1 = 4
Gradient = 8 / 4 = 2

## In practice

A road sign saying 10% gradient means the road rises 10 metres for every 100 metres across.

## Practice

### Flashcards

- **What is the gradient between (1, 2) and (5, 10)?** 2. The line rises 8 over a run of 4.

### Interview questions

**Find the equation of the straight line through (0, 3) and (2, 7).**

- Gradient = (7 - 3) / (2 - 0) = 2
- The line crosses the y-axis at 3
- So y = 2x + 3
- Check that (2, 7) fits: 2 x 2 + 3 = 7

## Questions people ask

### How do you calculate gradient from two points?

Divide the change in y by the change in x. Subtract the y values and the x values in the same order. Between (1, 2) and (5, 10), the change in y is 8 and the change in x is 4, giving a gradient of 2.

### What does a negative gradient mean?

A negative gradient means the line goes downhill when you read it from left to right. For every step across, the line drops. A gradient of -3 means the line falls 3 units for each 1 unit across. A zero gradient is a flat horizontal line.

## Related concepts

- [y = mx + c](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-3)
- [Parallel and perpendicular lines](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-4)
- [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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