Slope Calculator

m = (y₂−y₁) / (x₂−x₁). Returns slope-intercept form y = mx + b.

Inputs

Result

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General calculation reads

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How Not to Be Wrong
Jordan Ellenberg - math thinking
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The Joy of X
Steven Strogatz - accessible math
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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Enter two points.
  • Read slope, y-intercept, and full line equation.

About this calculator

Slope m = rise/run = Δy/Δx. Positive = uphill; negative = downhill; 0 = horizontal; undefined = vertical. Slope-intercept form y = mx + b is the standard line equation. Slope generalizes to derivatives in calculus (instantaneous rate of change). In real life: highway grades (often expressed in %), roof pitches, escalator angles.

Frequently asked

What does slope mean physically?+
Rate of change. m = 2 means y increases 2 for every 1 unit increase in x.
Why does vertical have undefined slope?+
Δx = 0 → division by zero. Vertical line equation is x = constant; no slope-intercept form possible.
Slope = grade %?+
Yes — 5% grade = slope 0.05. 100% grade = slope 1 = 45°. Highway "6% grade" warnings = significant downhill.
Parallel and perpendicular slopes?+
Parallel: same slope. Perpendicular: negative reciprocal (m₁ × m₂ = −1).
How does this connect to calculus?+
Slope between two points = average rate of change. As points → same x, you get derivative = instantaneous slope.

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