Calculate the slope (gradient), y-intercept, line equation, distance between two points, and angle of inclination.
Point 1: (x₁, y₁) and Point 2: (x₂, y₂)
| Property | Value |
|---|
Slope m = (y₂ − y₁) / (x₂ − x₁) = rise / run. In Australia, road gradients are often expressed as percentages (e.g. "10% grade" = slope of 0.1) or as ratios (e.g. "1:10").
Slope-intercept form: y = mx + b (b = y-intercept)
Point-slope form: y − y₁ = m(x − x₁)
Standard form: Ax + By = C
| Case | Slope |
|---|---|
| Horizontal line | m = 0 |
| Vertical line | m = undefined |
| Parallel lines | Equal slopes (m₁ = m₂) |
| Perpendicular lines | m₁ × m₂ = −1 |