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Slope From Two Points

Find the slope between two points as an exact fraction, plus the y-intercept, slope-intercept and point-slope forms, distance with a simplified radical, midpoint and angle of incline — with steps.

First point (x₁, y₁)

Second point (x₂, y₂)

Decimals and negative numbers are allowed. Two points with equal x give a vertical line.

Processing... 0%
Reading the two points
Computing Δy / Δx
Building the line equations
Done

Result

This page is the canonical two-point slope workflow: type (x₁, y₁) and (x₂, y₂) and the calculator substitutes them into m = (y₂ − y₁)/(x₂ − x₁), showing Δx and Δy separately before dividing. For (1, 2) and (4, 8) the working reads Δy = 6, Δx = 3, m = 6/3 = 2.

The slope arrives as an exact reduced fraction with its decimal value beside it, which is exactly the pair of answers a geometry or algebra assignment asks for. Decimal and negative coordinates are handled exactly, and two points with the same x give the honest verdict: the slope is undefined and the line is vertical, x = c.

Because the two points define everything about the line, the run continues past the slope: the equation in slope-intercept and point-slope forms, the y-intercept, the distance between the points as a simplified radical, the midpoint and the angle of incline in degrees — one input, the complete line.

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Executed in Browser

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Accepted Formats & Rules

  • Exact fraction arithmetic — decimal coordinates like 2.5 are stored as exact fractions, never rounded.
  • Vertical lines are reported honestly: undefined slope with the line equation x = c instead of a fake huge number.
  • Distance between the points is simplified as a radical (√45 → 3√5) with the decimal value next to it.

Key Benefits

✓ The slope comes out as an exact reduced fraction alongside its decimal value, with the Δy/Δx substitution written out step by step.
✓ One run gives the whole picture: y-intercept, slope-intercept form, point-slope form, distance with a simplified radical like 3√5, midpoint and angle of incline.
✓ Runs entirely in your browser: no sign-up, no uploads, instant results on any device.

Use Cases

  • • Find the slope through two points with the rise-over-run substitution shown — an exact fraction like 4/3 plus its decimal, ready for algebra homework.
  • • Turn two points into the line's equation in both slope-intercept (y = mx + b) and point-slope (y − y₁ = m(x − x₁)) forms with exact coefficients.
  • • Measure the segment between the points: distance as a simplified radical (3√5), the exact midpoint and the angle of incline in degrees.