How to Find the Slope of a Line (Step by Step)
Find the slope of a line from two points, a graph, an equation or a table — with the formula and worked examples.
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Frequently asked questions
What is the slope formula?
Slope m = (y₂ − y₁) ÷ (x₂ − x₁) — the change in y divided by the change in x between two points.
What does rise over run mean?
Rise is the vertical change between two points; run is the horizontal change. Slope is rise divided by run.
What is the slope of a horizontal line?
Zero. A horizontal line has no vertical change, so the rise is 0 and 0 ÷ run = 0.
Why is the slope of a vertical line undefined?
Because the run (change in x) is zero, and division by zero is undefined.
What does a negative slope mean?
The line falls from left to right — as x increases, y decreases.
How is slope used in y = mx + b?
m is the slope and b is the y-intercept. Knowing the slope and one point lets you find the full line equation.
Finding the slope of a line
Slope measures how steep a line is — how much it rises (or falls) for each step to the right. It is defined as rise over run: the change in y divided by the change in x. The formula between two points is m = (y₂ − y₁) ÷ (x₂ − x₁).
Worked example
For the points (1, 2) and (4, 11): the rise is 11 − 2 = 9 and the run is 4 − 1 = 3, so the slope is 9 ÷ 3 = 3. A slope of 3 means the line climbs three units up for every one unit across.
Reading the sign
A positive slope rises left to right; a negative slope falls. A horizontal line has a slope of 0 (no rise), and a vertical line has an undefined slope, because the run is zero and you cannot divide by zero.
In the equation y = mx + b, the slope m sits in front of x and b is the y-intercept. Once you know the slope and one point, you can write the whole equation of the line, which is why slope is central to coordinate geometry.
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