Slope Calculator
Enter two points. Get the slope, the equation of the line, the distance and the midpoint.
How it works
Slope is the change in y divided by the change in x. The y-intercept comes from putting one point into y = mx + b. A vertical line has no slope, so its equation is x = a number.
Example
Find the line through (−2, 5) and (4, −1).
y = −x + 3
- Slope
- −1
- y-intercept
- 3
- Distance
- 6√2 ≈ 8.4853
- Midpoint
- (1, 2)
Steps
- Change in y: −1 − 5 = −6. Change in x: 4 − (−2) = 6.
- Slope: m = −6 / 6 = −1.
- Find the y-intercept with the first point: b = 5 − (−1)·(−2) = 3.
More examples
Find the line through (0, 4) and (6, 4).
y = 4
- Slope
- 0
- y-intercept
- 4
- Distance
- 6
- Midpoint
- (3, 4)
Steps
- Change in y: 4 − 4 = 0. Change in x: 6 − 0 = 6.
- Slope: m = 0 / 6 = 0.
- Find the y-intercept with the first point: b = 4 − 0·0 = 4.
Find the line through (3, 1) and (3, 7).
x = 3
- Slope
- Undefined
- Distance
- 6
- Midpoint
- (3, 4)
Steps
- Change in y: 7 − 1 = 6. Change in x: 3 − 3 = 0.
- The change in x is 0, so the slope is undefined: this is a vertical line.
Common mistake
Subtract in the same order on top and bottom. Mixing them flips the sign of the slope.
Questions
What do the different slopes look like?
A positive slope rises left to right, a negative slope falls, and a slope of 0 is flat. A vertical line has an undefined slope.
How can I tell if two lines are parallel or perpendicular?
Parallel lines have the same slope. Perpendicular slopes multiply to −1, like 2 and −1/2.
Does it matter which point comes first?
No, as long as you subtract in the same order on top and bottom.