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?
The slope formula is m = (y₂ − y₁) ÷ (x₂ − x₁): the change in y divided by the change in x between two points on the line.
How do I find slope from two points?
Subtract the y‑values to get the rise, subtract the x‑values in the same order to get the run, then divide rise by run. For (2,3) and (6,11): (11−3)÷(6−2) = 8÷4 = 2.
How do I find slope from an equation?
Put the equation in the form y = mx + b. The coefficient of x is the slope. In y = 3x + 5 the slope is 3.
Does the order of the points matter?
No, as long as you are consistent. Whichever point you call the first, use its x and y first in both the top and bottom of the fraction.
What if the run is zero?
If the two points share the same x‑value, the run is zero and the slope is undefined — the line is vertical.
How to Find the Slope of a Line (Step by Step)
Slope tells you how steep a line is — how much it rises (or falls) for each step you take to the right. Once you know two things about a line, finding its slope takes only a moment. This guide shows you four ways to do it.
The slope formula
For any two points (x₁, y₁) and (x₂, y₂) on a line, the slope m is:
m = (y₂ − y₁) ÷ (x₂ − x₁) — that is, the change in y (the rise) divided by the change in x (the run).
Method 1: From two points
| Step | Action | Example with (2, 3) and (6, 11) |
|---|---|---|
| 1 | Label the points | (x₁, y₁) = (2, 3), (x₂, y₂) = (6, 11) |
| 2 | Find the rise (y₂ − y₁) | 11 − 3 = 8 |
| 3 | Find the run (x₂ − x₁) | 6 − 2 = 4 |
| 4 | Divide rise by run | 8 ÷ 4 = 2 |
The slope is 2: the line rises 2 units for every 1 unit it moves right.
Method 2: From a graph
Pick two points where the line crosses exact grid intersections. Count how far up or down you move to get from one to the other (the rise), then how far left or right (the run), and divide. Moving up is positive rise; moving down is negative.
Method 3: From an equation
If the line is written in slope‑intercept form, y = mx + b, the slope is simply the number multiplying x. In y = 3x + 5, the slope is 3. If the equation is in another form, rearrange it to isolate y first.
Method 4: From a table
Choose any two rows as your two points and apply the formula. If the slope is the same for every pair of rows, the relationship is linear.
Common mistakes to avoid
- Subtracting the x and y values in a different order — always keep the same point first in both the top and bottom.
- Mixing up rise and run (slope is rise over run, not run over rise).
- Forgetting that a vertical line has an undefined slope because the run is zero.
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