Slope formula
The slope formula measures how steep a line is. It is the change in y divided by the change in x between any two points on the line, often described as rise over run.
- m = the slope of the line
- (x₁, y₁) = the first point
- (x₂, y₂) = the second point
Rise over run
Slope is the vertical change (rise) divided by the horizontal change (run) as you move from one point to another. A slope of 2 means the line climbs 2 units for every 1 unit across. The steeper the line, the larger the absolute value of the slope.
Positive, negative, zero, and undefined
A positive slope rises from left to right; a negative slope falls. A horizontal line has a slope of zero, since y never changes. A vertical line has an undefined slope, because the run is zero and division by zero is not allowed. The sign and size of m capture the direction and steepness at once.
- Take the points (1, 2) and (4, 8).
- Change in y: 8 − 2 = 6.
- Change in x: 4 − 1 = 3.
- Slope: m = 6 / 3 = 2. The line rises 2 units for every 1 unit across.
Find a slope
Use the Slope Calculator, or see the Linear Equation Formula to build the full line equation.
FAQ
What is the slope formula?
m = (y₂ − y₁) / (x₂ − x₁), the change in y divided by the change in x between two points.
What does a negative slope mean?
The line falls from left to right: as x increases, y decreases.