How to find slope from a graph
Quick answer
Pick two points on the line, count how far you go up or down (the rise) and how far you go right (the run) between them, then divide: slope = rise ÷ run.
Step by step
- Pick two clear pointsChoose two points where the line crosses the grid exactly at a corner, so you can read their coordinates without guessing.
- Count the riseStarting at the left point, count how many units you move up (positive) or down (negative) to reach the height of the second point.
- Count the runCount how many units you move to the right to reach the second point.
- Divide rise by runSlope = rise ÷ run. Simplify the fraction if you can, for example 4/2 becomes 2.
Slope tells you how steep a line is and which way it tilts. On a graph, you can read it with nothing more than counting squares.
A worked example
Say a line passes through the points (1, 3) and (3, 7).
- From (1, 3) to (3, 7), you go up 4 units. That’s the rise.
- You go right 2 units. That’s the run.
- Slope = 4 ÷ 2 = 2.
Every time the line moves 1 step right, it climbs 2 steps up.
How to find the slope and y-intercept from a graph
The y-intercept is where the line crosses the vertical y-axis. Read the y value at that crossing point. In our example, the line crosses the y-axis at (0, 1), so the y-intercept is 1.
If the line doesn’t cross at a neat grid point, start from a known point and use the slope to step back to x = 0. From (1, 3), going 1 step left means going 2 steps down, which lands on (0, 1).
How to write slope-intercept form from a graph
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Plug in the two numbers you just found:
m = 2 and b = 1, so the equation of the line is y = 2x + 1.
That’s also how you find the equation of a line from a graph. To check it, put in a point you know: when x = 3, y = 2(3) + 1 = 7, which matches the point (3, 7).
The four kinds of slope
| Line looks like | Slope |
|---|---|
| Rises from left to right | Positive |
| Falls from left to right | Negative |
| Perfectly flat (horizontal) | Zero |
| Straight up and down (vertical) | Undefined |
A vertical line has no run at all, and you can’t divide by zero, which is why its slope is called undefined.
No graph, just numbers? Here’s how to find slope from two points using the formula, and how to find slope from a table.
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