What is slope?
Slope describes how steep a line is and which way it goes. It tells you how much y changes for every one-unit change in x. A slope of 3 means the line rises 3 units for each unit it moves right. Steeper lines have bigger slopes, and a flat line has a slope of 0.
The slope formula
m = (y₂ − y₁) ÷ (x₂ − x₁)
Once you know the slope, the y-intercept is b = y₁ − m × x₁, and the line's equation in slope-intercept form is y = mx + b.
Worked example
For the points (1, 2) and (3, 8):
- Rise: 8 − 2 = 6. Run: 3 − 1 = 2.
- Slope: 6 ÷ 2 = 3.
- Intercept: b = 2 − 3 × 1 = −1.
- Equation: y = 3x − 1.
Types of slope
- Positive: the line rises from left to right.
- Negative: the line falls from left to right.
- Zero: a horizontal line, y = constant.
- Undefined: a vertical line, x = constant.
Slope in real life
Slope shows up as the grade of a road, the pitch of a roof, the incline of a wheelchair ramp and the rate of change on any graph, like speed on a distance-time chart. Ramp and roof guides usually express slope as a ratio or a percentage, which is the slope multiplied by 100.
Last reviewed October 2026.