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# Gradient between two points
- URL: https://www.esheets.io/gradient-between-two-points/
- Published: 2025-01-20T22:53:37.000Z
- Updated: 2026-06-21T16:42:12.000Z
- Author: Richard Linnington
- Tags: Maths, Algebra, Geometry and Shape

The gradient between two points tells us how steep a line is when connecting them. It's like figuring out how quickly you're climbing or descending a hill when moving from one spot to another. Gradients are everywhere—whether you're driving uphill, designing ramps, or analyzing trends in data! [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise gradient between two points with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Finding the change in y.
- Finding the change in x.
- Using gradient = change in y / change in x.
- Interpreting positive, negative or zero gradients where relevant.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Calculate the gradient of the line segment connecting the two points.

  
## Topic guide

### What this worksheet practises

This worksheet provides practice on calculating the exact gradient (steepness) of a straight line connecting two coordinate points. This is identical to the "finding-the-gradient" topic, reinforcing the core coordinate geometry formula.

### Key method

The gradient formula is: Gradient (m) = (Change in y) ÷ (Change in x).

- Identify the coordinates of your two points: Point A (x₁, y₁) and Point B (x₂, y₂).
- Calculate the difference between the y-coordinates. This gives you the vertical "rise".
- Calculate the difference between the x-coordinates. This gives you the horizontal "run".
- Divide the y-difference by the x-difference. Be extremely careful with negative numbers during the subtraction.

### Worked example

**Find the gradient of the line connecting A(3, −1) and B(5, 7).**

Step 1: Calculate the change in y.

y of point B minus y of point A = 7 − (−1) = 7 + 1 = 8.

Step 2: Calculate the change in x. Because we started with point B for the y's, we must start with point B for the x's.

x of point B minus x of point A = 5 − 3 = 2.

Step 3: Calculate the gradient.

Gradient (m) = 8 ÷ 2 = 4.

### Common mistakes to avoid

The two most common errors are: 1) Dividing the change in x by the change in y (putting the run on top of the rise), and 2) Mixing up the order of the points halfway through. If you calculate (y₂ − y₁), you absolutely must calculate (x₂ − x₁). If you switch to (x₁ − x₂), your final answer will have the wrong sign.

### Things to remember

If your line goes downwards from left to right, your gradient must be a negative number. Always do a quick visual check (or sketch the points) to ensure the sign of your calculated gradient matches the physical reality of the line.