Slope Calculator
Slope, y-intercept and distance between two points on a line.
- Slope (m)2.0000
- y-intercept (b)0.0000
- Distance between points4.4721
Inputs used
- Point 1 — x1
- Point 1 — y2
- Point 2 — x3
- Point 2 — y6
About this calculator
The slope of the line through two points is rise over run: m = (y₂ − y₁) ÷ (x₂ − x₁). A slope of 2 means the line climbs 2 units for every 1 unit it moves right; negative slopes fall; zero is horizontal.
With the slope known, the y-intercept follows from either point: b = y − mx, giving the full line equation y = mx + b. The distance between the points comes from the Pythagorean theorem on the run and rise.
Two points with the same x-coordinate make a vertical line — its slope is undefined (division by zero), and the calculator reports an error rather than a made-up number.
Frequently asked questions
What is the formula for slope?
Slope is rise over run: m = (y₂ − y₁) ÷ (x₂ − x₁). For the points (1, 2) and (3, 6) that is (6 − 2) ÷ (3 − 1) = 4 ÷ 2 = 2.
What is the slope of a horizontal line?
Zero. A horizontal line has no rise, so y₂ − y₁ = 0 and the slope is 0 ÷ (x₂ − x₁) = 0 for any two of its points.
Why is the slope of a vertical line undefined?
A vertical line has two points with the same x-coordinate, so the run x₂ − x₁ is zero and the formula divides by zero. Division by zero has no value, so the slope is undefined rather than infinite.
How do I find the y-intercept from the slope?
Rearrange y = mx + b to b = y − mx using either point. For (1, 2) with slope 2, b = 2 − 2 × 1 = 0, giving the line equation y = 2x.
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Results are informational only — not financial, medical or legal advice.