Slope Calculator guide

Slope Formula — Rise Over Run From Two Points

The slope formula compares vertical change with horizontal change between two points on the same straight line.

The slope formula

m = (y₂ − y₁) / (x₂ − x₁). Here, Δy = y₂ − y₁ is the rise and Δx = x₂ − x₁ is the run.

Keep subtraction order consistent

If you reverse the points, reverse both the numerator and denominator. Both signs change, so the slope remains the same.

Rise over run

The coordinate formula and rise-over-run description are the same relationship: vertical change divided by horizontal change.

Simplify the fraction

For points (2, 3) and (7, 6), rise = 3 and run = 5, so slope = 3/5 = 0.6.

Positive, negative, zero, and undefined slope

Positive slopes rise left-to-right. Negative slopes fall. Horizontal lines have slope 0. Vertical lines have run 0, so division by zero makes slope undefined.

Vertical lines

A vertical line through x = 3 is written x = 3. Do not replace its undefined slope with 0 or Infinity.

Slope-intercept and point-slope forms

For nonvertical lines, slope-intercept form is y = mx + b. Point-slope form is y − y₁ = m(x − x₁). Both use the same exact slope.

Worked negative example

For (-2, 3) and (4, -1), Δy = -4 and Δx = 6, so the slope reduces to -2/3.