What Is Slope?
Slope measures how steep a line is, how much it rises (or falls) for every unit it moves to the right.
The formula
Slope = rise ÷ run = change in y ÷ change in x
Between two points (x₁, y₁) and (x₂, y₂):
m = (y₂ − y₁) / (x₂ − x₁)
Example: Points (1, 2) and (4, 8). m = (8 − 2) / (4 − 1) = 6/3 = 2.
The line rises 2 units for every 1 unit to the right.
Types of slope
| Slope | Looks like | Example |
|---|---|---|
| Positive | Goes up (left to right) | m = 2 |
| Negative | Goes down (left to right) | m = -3 |
| Zero | Horizontal (flat) | m = 0 |
| Undefined | Vertical | x = 5 |
Slope in y = mx + b
In slope-intercept form, the slope is the number in front of x:
- y = 2x + 1 → slope is 2 (rises steeply)
- y = 0.5x + 3 → slope is 0.5 (rises gently)
- y = -x + 4 → slope is -1 (falls at 45°)
Real-world slope
- A hill with slope 0.1 is gentle. Slope 2 is extremely steep.
- A roof with steeper slope sheds rain better.
- A road sign showing "8% grade" means the road rises 8 feet for every 100 feet of horizontal distance (slope = 0.08).
Related concepts
- Linear equations and graphing: full teaching guide
- Coordinate plane: where slope is visualized
- Ratios: slope is a ratio of vertical to horizontal change