Rates of Change and Gradient
The gradient of a straight line measures how steeply it rises or falls. Gradient represents a rate of change — how much the y-value changes for each unit increase in x.
What You Need to Know
Key Concept Diagram
Gradient = rise / run = (y2 - y1) / (x2 - x1)
Positive gradient means the line rises left to right; negative gradient means it falls
A gradient of zero means a horizontal line (no change)
The gradient equals the coefficient m in y = mx + c
Key Vocabulary
Gradient
The steepness of a line; rise divided by run
Rise
The vertical change between two points on a line
Run
The horizontal change between two points on a line
Rate of change
How quickly one quantity changes relative to another
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Find the gradient of the line passing through (2, 3) and (6, 11).
Question 2
A line has gradient -3 and passes through (0, 5). What is the equation of the line?
Question 3
A car travels 240 km in 3 hours. What is the gradient of its distance-time graph?
Key Concepts Summary
- ●Gradient = rise / run = (y2 - y1) / (x2 - x1)
- ●Positive gradient means the line rises left to right; negative gradient means it falls
- ●A gradient of zero means a horizontal line (no change)
- ●The gradient equals the coefficient m in y = mx + c