Slope calculator

Type two points, such as (-2, 3) and (2, 0). Brackets are optional, so four numbers in a row work too. The slope appears as you type.

Below it is the line in slope-intercept form, y = mx + b, with point-slope and standard form, the intercepts, the angle, the distance between the points and the midpoint. The graph draws the line with the rise and run marked.

Slope measures how steep a line is: how far it goes up for each step to the right. Take the change in y and divide it by the change in x, so m = (y₂ − y₁) ÷ (x₂ − x₁).

For (-2, 3) and (2, 0), the rise is 0 − 3 = −3 and the run is 2 − (−2) = 4. So the slope is −3/4. The line drops 3 for every 4 it moves right. It doesn't matter which point you call the first, as long as you subtract in the same order top and bottom.

Once you have m, put one point into y = mx + b to find b, the y-intercept. With m = −3/4 and the point (−2, 3), 3 = (−3/4)(−2) + b, so b = 3 − 3/2 = 3/2. The line is y = −(3/4)x + 3/2.

Multiply through to clear the fractions and you get the standard form, 3x + 4y = 6. Teachers often ask for that one.

A flat line has a rise of 0, so its slope is 0 and its equation is just y = a number. A vertical line has a run of 0. Dividing by 0 has no answer, so its slope is undefined, and its equation is x = a number.

Two lines are parallel when they have the same slope. They are perpendicular when the slopes multiply to −1, so a line with slope 2 meets one with slope −1/2 at a right angle.