From two points
The line through (1, 2) and (5, 10) has a slope of 2, an angle of about 63.4°, and the equation y = 2x.
Slope calculator
Result
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How it works
Slope is rise over run: how much y changes (Δy) for a given change in x (Δx). The angle of inclination is just the same ratio read as an angle, via the arctangent — a slope of 1 is a 45° line, since rise and run are equal.
Once the slope is known, the y-intercept follows by plugging either point back into y = mx + b and solving for b, which is exactly what pins the line to those specific points rather than just any line with that slope.
Formulas used
Slope
m = (y₂ − y₁) ÷ (x₂ − x₁)
Line equation
y = mx + b
Distance between two points
d = √((x₂ − x₁)² + (y₂ − y₁)²)
Worked examples
From a point and a slope
A line through (2, 3) with slope 2 has the equation y = 2x − 1.
Assumptions and limits
- The line is straight and lies in a standard xy-plane.
- For the point-and-slope mode, a second point one unit to the right is used only to draw the diagram, not as extra input.
Frequently asked questions
What does a negative slope mean?
The line falls as x increases, rather than rising — visually, it runs from upper-left to lower-right instead of lower-left to upper-right.
What is a slope of zero?
A perfectly horizontal line — y stays the same no matter how x changes.
Why does a vertical line have no slope?
Slope is rise over run, and a vertical line has zero run (Δx = 0) — dividing by zero is undefined, so a vertical line simply has no slope value, described instead as x = a constant.
How steep is a slope of 1?
Exactly 45° — rise and run are equal, so the line climbs at the same rate horizontally as it does vertically.
Updated
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