Calculate rise over run, segment length, and the equation of a line through two points.
Overview
Slope tells you how steep a line is and whether it rises or falls as x increases. In coordinate geometry, slope is the rate of change between two points, and it is the foundation for linear models in economics, physics, and data trends.
Given two points, rise over run gives m = (y2 - y1) / (x2 - x1). A positive slope climbs to the right, a negative slope descends, zero slope is horizontal, and undefined slope indicates a vertical line where x is constant.
This slope calculator also reports the distance between points and the slope-intercept equation when possible, so you can move from raw coordinates to a line you can graph or plug into spreadsheets. Always label which point is first; swapping points does not change slope but can affect how you interpret direction in applied problems.
In applications, slope is unit-dependent: dollars per month, meters per second, or temperature per hour. Keep units attached when you interpret results so the rate matches the story you are telling.
Steps
Input (x1, y1) coordinates.
Input (x2, y2) coordinates.
Compute m using change in y over change in x.
Check straight-line distance between the points.
Use slope-intercept or point-slope form as provided.
Plot both points to confirm sign and steepness visually.
Math
m = (y2 - y1) / (x2 - x1); d = sqrt((x2-x1)^2 + (y2-y1)^2)
Slope measures vertical change per horizontal change. Distance applies the Pythagorean theorem to the horizontal and vertical legs.
Worked cases
m = (15-3)/(8-2) = 12/6
Slope m = 2.
d = sqrt(6^2 + 12^2) = sqrt(180)
Distance ≈ 13.42 units.
m = 0/7 = 0
Slope = 0 (horizontal line).
Why use this
Questions