⭐ 0
🔍
Text Image PDF & Docs Audio Music Electronics Time Utilities Validators Esoteric Games

Slope-Intercept Form Calculator (y = mx + b)

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 slope-intercept card put first: enter two points and the tool derives the full equation y = mx + b. For (1, 2) and (4, 8) it computes m = (8 − 2)/(4 − 1) = 2 and b = 2 − 2·1 = 0, so the line is y = 2x.

Both coefficients are exact: the slope is a reduced fraction and the intercept comes from b = y₁ − m·x₁ carried out in fraction arithmetic, so points with decimal coordinates produce answers like y = (3/2)x − 1/4 rather than rounded approximations. The substitution steps for m and b are written out one per line.

Slope-intercept form is the version you graph from and the one most homework answers expect: m tells the steepness and b marks where the line crosses the y-axis — the run also reports that crossing point, the point-slope form, midpoint and distance from the same pair of points. If your two points share an x-coordinate, the tool honestly reports an undefined slope and gives the vertical line x = c instead.

🛡️
Executed in Browser

Your files and inputs never leave this device. Processing runs completely offline. 100% Secure.

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.