Slope calculator
Find the slope between two points and write the matching point-slope equation.
What this calculator covers
Use this slope calculator to measure the rise and run between two points and turn that ratio into the line's slope.
It also reports the point-slope equation, which makes the result useful for graphing and coordinate-geometry problems right away.
Frequently asked questions
- What does a negative slope mean?
- A negative slope means the line falls from left to right — as x increases, y decreases. The steeper the negative value, the faster the line descends across the coordinate plane.
- What happens if the two x-coordinates are the same?
- A vertical line has an undefined slope because the run is zero, which would require dividing by zero. The calculator rejects that input rather than returning an infinite or meaningless result.
- How do I find the y-intercept from the point-slope equation?
- Expand the point-slope form by distributing the slope and then moving the constant to the right side. For example, y − 2 = 3(x − 1) rearranges to y = 3x − 1, giving a y-intercept of −1.
- Does it matter which point I enter as (x1, y1)?
- No — the slope value is the same regardless of which point is labeled first. The point-slope equation will look different because it anchors to (x1, y1), but both forms describe the identical line.
Tool
Run the calculation
Result
RESULT · SLOPE
â„–215
Primary result
2
From (1, 2) to (5, 10), the line rises 8 over a run of 4, so the slope is 2.
- Slope
- 2
- Rise
- 8
- Run
- 4
- Point-slope equation
- y - 2 = 2(x - 1)
Step-by-step solution
- 1.Compute the horizontal change: 5 - 1 = 4.
- 2.Compute the vertical change: 10 - 2 = 8.
- 3.Divide rise by run to get m = 8 / 4 = 2, and write the line as y - 2 = 2(x - 1).
Walkthrough
Visual walkthrough
Slope is a ratio: measure the rise between the points, measure the run, then divide.
01
Measure the run
5 - 1 = 4
The run tracks how far the line moves horizontally between the two points.
02
Measure the rise
10 - 2 = 8
The rise tracks how far the line moves vertically across the same interval.
03
Divide rise by run
That ratio is the slope, and the same point pair also gives a point-slope equation for the line.
m = 2 · y - 2 = 2(x - 1)