Mathematics · Algebra
Slope, Distance & Midpoint Calculator — Line Through Two Points
Enter two points to get the slope (as a fraction when possible), the distance between them, the midpoint, the angle of the line, and its equation as y = mx + c and Ax + By = C, with the x- and y-intercepts. Vertical and horizontal lines are handled.
Your inputs
Quick start — try a typical case
Your result Live
Slope (m)
4/3
Rise 8 over run 6 = 1.3333333
- Distance
- 10 — √(6² + 8²)
- Midpoint
- (5, 7)
- Equation
- y = 1.3333333x + 0.33333333
- Standard Form
- 4x − 3y = −1
- Angle With the x-axis
- 53.1301°
- Intercepts
- x-intercept -0.25 · y-intercept 0.33333333
- Perpendicular Slope
- -0.75
How this is calculated
m = (y₂ − y₁) ÷ (x₂ − x₁) · d = √((x₂ − x₁)² + (y₂ − y₁)²) · midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2) · y = mx + c, c = y₁ − m·x₁
- m
- Slope (gradient): rise over run
The slope is how far the line rises for each step to the right: the change in y divided by the change in x. The distance between the points comes from Pythagoras, the midpoint is the average of the coordinates, and putting the slope and one point into y = mx + c gives the line's equation.
Assumptions & sources
- Points in a flat x–y plane.
Calculator ID MATH-SLOPE-001 · version 1.0.0
Common questions
What's the slope between (2, 3) and (8, 11)?
(11 − 3) ÷ (8 − 2) = 8/6 = 4/3.
What does an undefined slope mean?
The line is vertical — x doesn't change, so you'd divide by zero.
How are perpendicular slopes related?
They multiply to −1: a line of slope 4/3 is perpendicular to one of slope −3/4.