How to Find the Slope From Two Points (Formula + Examples)

To find the slope between two points (x₁, y₁) and (x₂, y₂), use the slope formula m = (y₂ − y₁) / (x₂ − x₁). Subtract the y-values on top, subtract the x-values on the bottom in the same order, and simplify. The result tells you how steep the line is and whether it goes up or down.

Worked example: slope between (1, 3) and (4, 9)

Find the slope of the line passing through (1, 3) and (4, 9).

1. Label the points: (x₁, y₁) = (1, 3) and (x₂, y₂) = (4, 9).
2. Apply the formula: m = (y₂ − y₁) / (x₂ − x₁) = (9 − 3) / (4 − 1).
3. Simplify the numerator and denominator: m = 6 / 3.
4. Reduce: m = 2.

The slope is 2, meaning the line rises 2 units for every 1 unit it moves right.

The slope formula, step by step

1. Label your two points. Pick one to be (x₁, y₁) and the other (x₂, y₂). Example: for (2, 5) and (6, 13), let (x₁, y₁) = (2, 5).
2. Subtract the y-values on top. Compute y₂ − y₁. Example: 13 − 5 = 8.
3. Subtract the x-values on the bottom, in the same order. Compute x₂ − x₁. Example: 6 − 2 = 4.
4. Divide to get the slope. m = (y₂ − y₁)/(x₂ − x₁). Example: 8 / 4 = 2.
5. Simplify the fraction if needed. Keep it as a fraction or integer; do not round unless asked. Example: 6/9 becomes 2/3.

Reading rise over run from a graph

The slope m = rise/run is exactly what the formula computes. The rise is y₂ − y₁ (vertical change) and the run is x₂ − x₁ (horizontal change). A positive slope goes up left-to-right; a negative slope goes down.

Second worked example: slope between (−2, 5) and (3, −5)

Find the slope through (−2, 5) and (3, −5).

1. Label: (x₁, y₁) = (−2, 5), (x₂, y₂) = (3, −5).
2. Top: y₂ − y₁ = −5 − 5 = −10.
3. Bottom: x₂ − x₁ = 3 − (−2) = 5.
4. Divide: m = −10 / 5 = −2.

The slope is −2. The line falls 2 units for every 1 unit right.

Common mistakes when computing slope

• Flipping rise and run. Slope is (y₂ − y₁)/(x₂ − x₁), not (x₂ − x₁)/(y₂ − y₁). Between (1, 3) and (4, 9), the slope is 6/3 = 2, not 3/6 = 1/2.
• Subtracting in different orders on top and bottom. If you do y₂ − y₁ up top, you must do x₂ − x₁ below — not x₁ − x₂. Otherwise the sign flips.
• Sign errors with negatives. 3 − (−2) is 5, not 1. Rewrite subtraction of a negative as addition.
• Confusing horizontal and vertical lines. A horizontal line (like y = 4) has slope 0. A vertical line (like x = 4) has an undefined slope because the run is 0.
• Forgetting to simplify. A slope of 4/6 should be written as 2/3.

Now that you have seen the formula applied twice, the fastest way to lock it in is to try a few problems where a tutor catches your slip-ups in real time. Sign up to practice finding slope from two points with LernOS's guided step-by-step tutor — it will walk you through each subtraction and ask you the right question the moment you get stuck.