Slope Calculator
Find the slope of a line through two points — plus the y-intercept, the slope-intercept form (y = mx + b), and the angle of inclination.
What is Slope Calculator?
The slope calculator finds the steepness of the line through two points (x₁, y₁) and (x₂, y₂). Slope is the rate of change of y with respect to x — the most-asked algebra concept on the SAT and ACT.
Formula
Slope formula:
m = (y₂ − y₁) ÷ (x₂ − x₁)
Once you have m, the y-intercept b comes from plugging either point back into y = mx + b: b = y₁ − m × x₁.
A vertical line (x₁ = x₂) has undefined slope. A horizontal line (y₁ = y₂) has slope 0.
Worked example
Points (1, 2) and (4, 8):
- m = (8 − 2) ÷ (4 − 1) = 6 ÷ 3 = 2
- b = 2 − 2 × 1 = 0
- Equation: y = 2x
- Angle: arctan(2) ≈ 63.43°
How to use this calculator
- Enter the coordinates of two distinct points on the line.
- The calculator returns slope, y-intercept, the full slope-intercept equation, and the angle the line makes with the positive x-axis.
Frequently asked questions
What does a positive vs negative slope mean?
Positive = line rises left to right. Negative = line falls. Zero = horizontal. Undefined = vertical.
What does the y-intercept tell me?
It's where the line crosses the y-axis (x = 0). In a real-world model, it's the starting value before any change in x.
How is slope used in real life?
Roof pitch, road grades, ramps and accessibility (ADA wheelchair ramps max out at 1:12 slope), economics (marginal rates), and any graph showing change over time.
Slope vs gradient vs derivative — same thing?
For a straight line, all three terms describe the same number. For curves, gradient and derivative refer to instantaneous slope at a specific point — calculus territory.