Slope Calculator — Line Equation, Distance & Midpoint

Slope (m) measures the steepness and direction of a line. It is calculated as the "rise over run": m = (y₂ - y₁) / (x₂ - x₁). A positive slope means the line rises left to right; negative means it falls; zero means horizontal; undefined means vertical.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis). Given two points, you can find m, then solve for b using one of the points.

The midpoint formula: M = ((x₁+x₂)/2, (y₁+y₂)/2). It gives the point exactly halfway between two points on the coordinate plane.

Using the Pythagorean theorem: d = √((x₂-x₁)² + (y₂-y₁)²). This is called the Euclidean distance.

Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals: if one line has slope m, the perpendicular slope is -1/m. For example, slopes 2 and -1/2 are perpendicular.