Algebra
Slope between two points
Rise divided by run. Take both differences in the same direction, or the sign reverses.
The Formula
m = (y2 - y1) / (x2 - x1)
Rise divided by run. Take both differences in the same direction, or the sign reverses.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| x1, y1 | Coordinates of the first point | coordinates | Order does not matter as long as both differences are taken the same way. |
| x2, y2 | Coordinates of the second point | coordinates | If x2 equals x1 the line is vertical and the slope is undefined. |
| m | Slope of the line | units of y per unit of x | Positive slopes rise left to right; negative slopes fall. |
What Each Symbol Means
x1, y1coordinates
Coordinates of the first point
Order does not matter as long as both differences are taken the same way.
x2, y2coordinates
Coordinates of the second point
If x2 equals x1 the line is vertical and the slope is undefined.
munits of y per unit of x
Slope of the line
Positive slopes rise left to right; negative slopes fall.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate slope page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Slope, filed under Math. Every number the guide produces comes from substituting into this one line.