How to use the Slope Calculator
Enter x and y for two points on the line. The result is the slope, how much y changes for each step in x.
Worked example
Between (1, 2) and (4, 11), y rises 9 while x rises 3, so the slope is 9 ÷ 3 = 3. The line rises 3 units for every 1 unit to the right. Using the first point, the equation of the line is y = 3x − 1.
Reading the sign and size
A positive slope goes up from left to right and a negative one goes down. Zero means a flat line. Slope also describes real grades: a road that climbs 5 m over 100 m has a slope of 0.05, written as a 5% grade, and ramps for wheelchair access are usually kept much gentler than that.
The formula
m = (y₂ − y₁) ÷ (x₂ − x₁)
Examples
- Points (0, 0) and (4, 3)
Slope: 0.75
- Points (1, 2) and (5, 10)
Slope: 2
- Points (2, 9) and (6, 1), a falling line
Slope: -2
Limitations and assumptions
The two x values must differ. A vertical line has an undefined slope.
Frequently asked questions
What is the slope formula?
m = (y2 − y1) ÷ (x2 − x1).
What does a negative slope mean?
The line falls as x increases. A positive slope rises, a zero slope is flat.
What if the two x values are equal?
The line is vertical and its slope is undefined, because the run is zero.
How do I get the line equation?
Use y − y1 = m(x − x1), or compute the slope here and substitute either point.