Slope Calculator

Calculate the slope, y-intercept, distance, and equation of a line from two points on a coordinate plane.

X-coordinate of the first point.

Y-coordinate of the first point.

X-coordinate of the second point.

Y-coordinate of the second point.

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How to Calculate Slope

Slope measures the steepness and direction of a line. The formula is m = (y₂ - y₁) / (x₂ - x₁), or "rise over run." A positive slope goes upward left to right, a negative slope goes downward, zero slope is horizontal, and undefined slope is vertical.

Slope-Intercept Form

The slope-intercept form of a line 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, first calculate the slope, then substitute one point into y = mx + b to solve for b.

Point-Slope Form

The point-slope form is y - y₁ = m(x - x₁), useful when you know the slope and one point. It can be converted to slope-intercept form by distributing m and adding y₁ to both sides. Both forms describe the same line.

Parallel and Perpendicular Lines

Parallel lines have equal slopes (m₁ = m₂). Perpendicular lines have negative reciprocal slopes (m₁ × m₂ = -1). For example, a line with slope 2 is perpendicular to a line with slope -1/2. These relationships are fundamental in geometry and coordinate proofs.

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