Geometry
Class 10-11

Slope of a Line

m=y2y1x2x1=tanθm = \frac{y_2-y_1}{x_2-x_1} = \tan\theta
01234511.522.533.544.55
m = (y₂-y₁)/(x₂-x₁) = tan(θ)

Adjust Variables

Point 1 y
y1 =
-1010
Point 2 y
y2 =
-1010

Slope measures steepness of a line. Positive slope = rising line; negative = falling; zero = horizontal; undefined = vertical.

Real-World Applications

Road gradients — Highway signs showing 6% grade mean slope = 0.06.

Wheelchair ramps — ADA requires maximum slope of 1:12 (about 4.8°).

Roofing — Roof pitch expressed as rise over run.

Economics — Marginal cost as slope of total cost curve.

Physics — Velocity from position-time graph slope.

Skiing — Slope difficulty ratings based on steepness.

Drainage — Minimum slopes for water flow.

Stairs — Building codes specify max rise/run ratios.

Medicine — Dosage response curve steepness.

Finance — Trend lines in stock price analysis.

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