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Point-Slope Form Calculator

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 opens the slope calculator with the point-slope card put first: from two points it computes the exact slope m = Δy/Δx and writes the line as y − y₁ = m(x − x₁) using your first point. For (1, 2) and (4, 8) that is y − 2 = 2(x − 1).

Point-slope form is the natural intermediate step of coordinate geometry: it holds the slope and one known point without any rearranging, which makes it the fastest form to write down in a proof or a calculus problem before expanding. Negative coordinates fold into the signs correctly — a point like (−3, −1) produces y + 1 = m(x + 3).

The same run also expands the equation into slope-intercept form so you can compare the two, and adds the y-intercept, distance, midpoint and angle cards. Fractional slopes stay exact, so a line through (0, 0) and (3, 2) is reported as y = (2/3)x, never 0.6667x.

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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.