Slope Calculator

What Slope Means

Slope measures how steep a line is - how much it climbs for every step you take to the right. People call it “rise over run”: the rise is how far the line goes up, and the run is how far it goes across.

$$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$$

A bigger number means a steeper line. A positive slope climbs from left to right, a negative slope falls, a zero slope is flat, and a straight-up vertical line has no slope at all - its run is zero, and you cannot divide by zero. The graph by the calculator plots your two points and draws the rise and run as a little right triangle, so you can see exactly where the number comes from.

The Formula

$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}} \qquad b = y_1 - m x_1$$

How to Use It

1. Enter the coordinates of point 1 (x1, y1) and point 2 (x2, y2).
2. Read the slope and the line equation.

Worked Examples

Point 1	Point 2	Slope	Line
(1, 1)	(3, 5)	2	y = 2x − 1
(0, 0)	(4, 2)	0.5	y = 0.5x
(2, 5)	(6, 5)	0	y = 5
(3, 1)	(3, 7)	undefined	vertical line

FAQ

How do you calculate slope?

Divide the rise by the run: $\frac{y_2 - y_1}{x_2 - x_1}$. For (1, 1) and (3, 5): $\frac{4}{2} = 2$.

What does a negative slope mean?

The line goes down from left to right. A positive slope goes up.

Why is the slope of a vertical line undefined?

The run (x2 − x1) is zero, and dividing by zero is undefined. A horizontal line has a slope of 0 instead, because the rise is zero.