Slope Calculator

Mastering Slope and Linear Equations: Complete Guide

Slope is a fundamental concept in algebra and geometry that measures the steepness and direction of a line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points. This Professional Slope Calculator computes not only the slope but also the distance, midpoint, angle, and the complete equation of the line in slope‑intercept, point‑slope, and standard forms—all with a visual graph.

Slope Formula

The slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is m = (y₂ − y₁) / (x₂ − x₁). If the denominator is zero, the line is vertical and the slope is undefined. A positive slope rises from left to right; a negative slope falls; zero slope is horizontal.

Forms of Linear Equations

• Slope‑Intercept Form: y = mx + b, where m is slope and b is the y‑intercept.
• Point‑Slope Form: y − y₁ = m(x − x₁). Useful when you know a point and the slope.
• Standard Form: Ax + By = C, with integers A, B, C and A ≥ 0.

Distance and Midpoint

The distance between two points is given by the Pythagorean theorem: d = √[(x₂−x₁)² + (y₂−y₁)²]. The midpoint is the average of the coordinates: M = ((x₁+x₂)/2, (y₁+y₂)/2).

Slope as an Angle and Percentage

The angle of inclination is θ = arctan(m) (in degrees). Percent slope, used in engineering and road grades, is |m| × 100%. A slope of 1 corresponds to a 45° angle and a 100% grade.