How to find slope from two points
Quick answer
Use the slope formula: m = (y₂ − y₁) ÷ (x₂ − x₁). Subtract the y values, subtract the x values in the same order, then divide.
Step by step
- Label the pointsCall the first point (x₁, y₁) and the second point (x₂, y₂). It doesn’t matter which one you call first.
- Subtract the y valuesWork out y₂ − y₁. This is the rise.
- Subtract the x values in the same orderWork out x₂ − x₁. This is the run.
- DivideSlope m = rise ÷ run. Simplify the fraction.
The formula is just “rise over run” written with numbers instead of squares on a graph. If you can subtract and divide, you can do this.
Example 1: a positive slope
Find the slope between (2, 3) and (6, 11).
- y₂ − y₁ = 11 − 3 = 8
- x₂ − x₁ = 6 − 2 = 4
- m = 8 ÷ 4 = 2
Example 2: a negative slope
Find the slope between (−1, 4) and (3, −4).
- y₂ − y₁ = −4 − 4 = −8
- x₂ − x₁ = 3 − (−1) = 4
- m = −8 ÷ 4 = −2
A negative slope means the line falls as you move to the right.
Mistakes to watch for
- Mixing the order. If you start with the second point’s y value on top, you must start with the second point’s x value on the bottom too. Swapping only one gives the wrong sign.
- Double negatives. Subtracting a negative number means adding: 3 − (−1) = 4, not 2.
- Same x values. If both points have the same x, the bottom of the fraction is zero. That’s a vertical line, and its slope is undefined.
Once you have the slope, you can build the full equation in y = mx + b form. Plug in one point to solve for b: using (2, 3) from Example 1, 3 = 2(2) + b, so b = −1 and the line is y = 2x − 1.
Working from a picture instead? See how to find slope from a graph.
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