Read slope as rise over run

Slope compares vertical change to horizontal change. It is not just steepness; the sign and special cases describe how the line moves from left to right.

Calculate slope from two points

Enter (x1, y1) and (x2, y2).
Subtract y-values to get rise.
Subtract x-values to get run.
Divide only if run is not zero.

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Rise, run, and slope

Use the same coordinate order for rise and run so the sign stays correct.

Rise

rise = y_{2} - y_{1}

Run

run = x_{2} - x_{1}

Slope

m = \frac{rise}{run} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

Example

m = \frac{- 6}{6} = - 1

Special cases

run = 0 \to undefined; rise = 0 and run \neq 0 \to m = 0

Interpret the result

Positive slope rises from left to right.
Negative slope falls from left to right.
Zero slope is horizontal.
Undefined slope is vertical.

FAQ

Does coordinate order matter?

You can label either point as point 1, but use the same order for rise and run. Reversing both differences keeps the same slope; mixing the order flips the sign.

Is undefined slope the same as zero slope?

No. Zero slope means a horizontal line with no rise. Undefined slope means a vertical line with zero run, so division by zero would be required.

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