Slope Calculator
Calculate the slope (rise over run) between two points, find the slope-intercept form of the line (y = mx + b), the distance between the points, and the midpoint.
Slope Formula
Slope m = (y₂ − y₁) / (x₂ − x₁) = rise / run
- Positive slope: Line goes up from left to right
- Negative slope: Line goes down from left to right
- Zero slope: Horizontal line
- Undefined slope: Vertical line (x₁ = x₂)
Frequently Asked Questions
Slope is the rate of change — how much y changes for every unit increase in x. A slope of 2 means y increases by 2 for every 1-unit increase in x.
y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).
The formula
Slope measures steepness: how much the line rises for each unit it moves right. It is often described as "rise over run".
Worked example
Through (2, 3) and (6, 11):
m = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2
A slope of 2 means the line climbs 2 units for every 1 unit right.
The order of the points doesn't matter, as long as you're consistent. Reversing both gives (3 − 11) ÷ (2 − 6) = −8 ÷ −4 = 2, the same answer. Reversing only one is the classic error and flips the sign.
Reading the sign
| Slope | The line |
|---|---|
| Positive | Rises left to right |
| Negative | Falls left to right |
| Zero | Horizontal |
| Undefined | Vertical |
A vertical line is undefined rather than infinite because x₂ − x₁ = 0, and division by zero has no value. The run is zero, so there is no rate of change to report.
Writing the equation of the line
With a slope and one point, point-slope form gives the equation directly:
Using m = 2 and the point (2, 3): y − 3 = 2(x − 2), which rearranges to y = 2x − 1. That is slope-intercept form, y = mx + b, where b = −1 is where the line crosses the y-axis.
Parallel and perpendicular
Parallel lines share the same slope. Perpendicular lines have slopes that are negative reciprocals — multiply to −1. A line perpendicular to slope 2 has slope −1/2.
Slope outside maths class
Roof pitch is slope expressed as rise per 12 inches of run. Road gradients are slope as a percentage — a 6% grade climbs 6 feet per 100 travelled. Accessibility ramps are governed by maximum slope rules. In statistics, the slope of a regression line is the effect size: how much the outcome changes per unit of the predictor.