Slope Intercept Calculator

Rise over run: the change in y divided by the change in x. From (0,0) to (2,4) the rise is 4 and the run is 2, so the slope is 2.

y = mx + b, where m is the slope and b is where the line crosses the y-axis. It is the most useful form for sketching a line, because both pieces of information are visible.

Undefined, not infinite. The run is zero, and division by zero has no answer rather than a very large one. A vertical line cannot be written in slope-intercept form at all.

Take the negative reciprocal. Perpendicular slopes multiply to −1, so the perpendicular to a slope of 2 is −0.5. It follows directly from the rise-over-run definition.

The same slope and a different intercept. If both the slope and intercept match they are the same line rather than parallel lines.

y − y₁ = m(x − x₁), which is more convenient when you know a point and the slope rather than the intercept. It rearranges to slope-intercept form in one step.

Ax + By = C, which handles vertical lines that slope-intercept form cannot and which makes finding both intercepts straightforward. It is preferred in linear programming for that reason.

Set the two equations equal and solve for x, then substitute back for y. Parallel lines give no solution, which shows up as an equation with no x term left.

The line falls from left to right — y decreases as x increases. The steeper the fall, the more negative the number.

A rate of change: distance per unit time, cost per unit produced, rise per unit run. Every linear relationship has a slope with units attached.

The same idea in different notation. A 1 in 12 ramp gradient is a slope of 0.0833, and a percentage grade is the slope times 100 — an 8.33% grade.

A line fitted through scattered points to minimise the total squared vertical distance. It has a slope and intercept exactly like any line, computed from the data rather than from two chosen points.