Gradient is change in y over change in x; in y = mx + c, m is the gradient and c is where the line crosses the y-axis.
What you will learn
- Find a gradient from two points or a drawn line
- Read m and c from y = mx + c, including rearranged equations
- Match equations to lines
- Test whether a point lies on a line
Gradient: up over across
The gradient measures steepness: how far the line goes up for every 1 across.
gradient = change in y ÷ change in x
- A(1, 2) and B(5, 10)
- change in y: 10 − 2 = 8
- change in x: 5 − 1 = 4
- gradient = 8 ÷ 4 = 2
A line sloping down from left to right has a negative gradient. Gradients can be fractions: from (0, 1) to (4, 4) is 3 up for 4 across, a gradient of 3/4. Subtract in the same order top and bottom, and always put the change in y on top.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Gradient: up over across
- Reading m and c
- Is a point on the line?
- Try it: Drive the line with m and c
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Down
In this unit: Straight-line graphs
Coordinates and midpoints, gradients and intercepts, the equation of a line, parallel and perpendicular lines, and straight-line graphs in real life.