Slope Calculator
Find the slope (m), angle, distance, and line equation (y = mx + b) passing through any two coordinate points (x₁, y₁) and (x₂, y₂).
See also: Ableitung Rechner, Proportion Calculator, Concrete Calculator
How it is calculated
Slope m = (y₂ − y₁) ÷ (x₂ − x₁); Angle θ = arctan(m); Distance d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Worked example: Finding the Slope Between Points (2, 3) and (8, 15)
Point 1: (2, 3), Point 2: (8, 15).
- Find Δy (rise): 15 − 3 = 12.
- Find Δx (run): 8 − 2 = 6.
- Compute slope: m = 12 ÷ 6 = 2.
- Calculate angle of inclination: arctan(2) = 63.43°.
- Determine Y-intercept: y = mx + b → 3 = 2(2) + b → b = −1.
- Form the slope-intercept line equation: y = 2x − 1.
Slope m = 2, Line equation: y = 2x − 1.
Frequently asked questions
What does a negative slope mean?
A negative slope means the line slants downwards from left to right, indicating that as X increases, Y decreases.
What is the slope of a flat horizontal line?
A horizontal line has a slope of 0 because the vertical rise is zero (0 ÷ Δx = 0).
What is the slope of a vertical line?
A vertical line has an undefined slope, because the run (change in X) is 0 and division by zero is impossible. The line equation is simply x = x1, and the angle of inclination is 90 degrees.
How is the angle of inclination calculated?
The angle is the arctangent of the slope, converted to degrees. For example, a slope of 2 gives an angle of 63.43 degrees.
How do I get the line equation from two points?
First find the slope m = (y2 minus y1) divided by (x2 minus x1), then find the intercept b = y1 minus m times x1. That gives the slope-intercept equation y = mx + b. For points (2, 3) and (8, 15), the equation is y = 2x minus 1.
Does the order of the two points matter?
No. Swapping the two points flips the signs of the rise and the run together, so the slope stays exactly the same.