How to find the slope of a line
- Enter the coordinates of two points on the line, (x₁, y₁) and (x₂, y₂). Negative numbers and decimals are fine.
- Read the slope as a fraction and a decimal, and the equation of the line in slope-intercept form y = mx + b.
- The table adds the angle, grade, intercepts, distance, midpoint and the slope of a perpendicular line, and the graph shows the line through both points.
The slope formula
Slope measures steepness: how much y changes for each unit of x. It is "rise over run", m = (y₂ − y₁) ÷ (x₂ − x₁). For the points (1, 2) and (4, 8), the rise is 6 and the run is 3, so the slope is 2: the line climbs two units for every unit to the right. A positive slope rises from left to right, a negative slope falls, zero is horizontal, and a vertical line has an undefined slope because the run is zero.
Once you know the slope, the y-intercept follows from b = y₁ − m·x₁, giving the full equation y = mx + b. Perpendicular lines have slopes that are negative reciprocals (2 and −1/2). The angle of inclination is the arctangent of the slope, and the grade used for roads and ramps is the slope as a percentage: a 1:12 wheelchair ramp is a grade of about 8.3%. Calculations are done in your browser.
What does a slope of 0 mean?
The line is horizontal: y does not change as x changes.
Why is the slope of a vertical line undefined?
The run (x₂ − x₁) is zero, and you cannot divide by zero.
How do I convert slope to an angle?
Angle = arctan(slope). A slope of 1 is 45°.