Gradient of a Line
The gradient of a line measures its steepness and direction. It is calculated as the rise (vertical change) divided by the run (horizontal change) between any two points on the line.
What You Need to Know
Key Concept Diagram
Gradient = rise / run = (y2 - y1) / (x2 - x1)
A positive gradient means the line goes uphill from left to right
A negative gradient means the line goes downhill from left to right
A horizontal line has gradient 0; a vertical line has an undefined gradient
Key Vocabulary
Gradient
The steepness of a line; the ratio of vertical rise to horizontal run
Rise
The vertical change between two points on a line (y2 - y1)
Run
The horizontal change between two points on a line (x2 - x1)
Intercept
The point where a line crosses an axis; the y-intercept is where x = 0
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A line passes through (1, 2) and (4, 8). What is the gradient?
Question 2
A line goes from (0, 5) to (3, 2). Is the gradient positive or negative?
Question 3
What is the gradient of a horizontal line?
Key Concepts Summary
- ●Gradient = rise / run = (y2 - y1) / (x2 - x1)
- ●A positive gradient means the line goes uphill from left to right
- ●A negative gradient means the line goes downhill from left to right
- ●A horizontal line has gradient 0; a vertical line has an undefined gradient