Slope as Rate of Change

Slope, m = rise ÷ run, is the fundamental measure of how one quantity changes relative to another. In algebra it describes lines; in the real world it is speed, price, gradient, or a rate — the steeper the slope, the faster the change.

From Two Points to a Line

Two points define a unique line. From the slope and one point you get the intercept, b = y1 − m·x1, producing the slope-intercept form y = mx + b. Distance and midpoint come from the same two points via the distance formula and averaging coordinates.

Degrees of Steepness

The angle from horizontal, arctan(m), connects slope to trigonometry and engineering grades. A 100% grade (45°) corresponds to m = 1; a vertical line has no finite slope at all.