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.

This on the SAT

The Digital SAT tests slope in its Algebra domain, typically with wording like The graph of the linear function f is shown in the xy-plane. What is the slope of the graph of f? or the table variant, The table shows selected values of a linear function f. What is the slope of f? The formula is exactly the one above — pick any two rows from the table, or two lattice points off the graph, and plug into m = (y₂ − y₁)/(x₂ − x₁).

The abstract-parameter version is a favorite SAT trap: Line ℓ contains the points (a, b) and (c, d) in the xy-plane, where a ≠ c. What is the slope of ℓ in terms of a, b, c, and d? The answer is (d − b)/(c − a). About half of missed responses swap the subtraction order or flip rise and run — the same errors listed above, just with letters instead of numbers. Bluebook (the digital testing app) ships with Desmos and lets you use it on every question, so on numeric graph or table problems you can plot two points and read the slope off the calculator in about ten seconds; the abstract-parameter version needs algebra, not graphing.

Working through the Advanced Math domain too? See our SAT-scoped guides on how to find the vertex of a parabola on the SAT and how to find the discriminant on the SAT.

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.