Skip to main content
MathidiaMathematics Academy
Linear graphs
Lesson 33 of 75
Standard practice

Understand gradient

Objective. Interpret gradient as a rate of change.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Gradient measures how steep a straight line is, found as the amount y changes divided by the amount x changes between two points. A positive gradient rises left to right and a negative gradient falls; the value tells you the rate of change, such as speed or cost per item. Between the points (1, 2) and (3, 8), the gradient is (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3. Always divide the change in y by the matching change in x, keeping the order consistent.

Worked example

Find the gradient of the line passing through the points (2, 1) and (5, 10).

2 … 1
Coordinate grid with the line 2 … 1
  1. 1Find the change in y: 10 − 1 = 9
  2. 2Find the change in x: 5 − 2 = 3
  3. 3Divide change in y by change in x: 9 ÷ 3
  4. 4The gradient is 3

Answer: 3

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils often divide the x-change by the y-change instead of the other way round, turning a gradient of 3 into 1/3. Always remember gradient is 'rise over run', change in y over change in x.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard