Slope Calculator
Calculate the slope, y-intercept and equation of a line through two (x, y) points.
- Rise (Δy)9
- Run (Δx)3
Slope is rise over run — here the line rises 9 for every 3 it runs, so the rise bar is the bigger of the two.
- Y-Intercept (b)-1
- Line Equationy = 3x − 1
- Distance Between Points9.4868
For every 3 units you move right, the line moves 9 units up — that's literally what "rise over run" means.
ƒShow your work
- 1Rise: Δy = y₂ − y₁ = 11 − 2 = 9
- 2Run: Δx = x₂ − x₁ = 4 − 1 = 3
- 3Slope: m = rise / run = 9 / 3 = 3
- 4Intercept: b = y₁ − m×x₁ = 2 − (3)(1) = -1
About the Slope Calculator
Slope measures how steep a line is — how much it rises or falls for every unit it moves sideways — and it's one of the first genuinely useful pieces of algebra, because it describes rate of change in general, not just lines on graph paper. Speed is the slope of a distance-vs-time line, a ramp's steepness is a slope, and a hillside's grade is a slope expressed as a percentage.
Students meet this calculating slope between two points for algebra homework, but it comes up constantly outside class too: a contractor checking that a wheelchair ramp meets accessibility requirements, a roofer calculating pitch, or anyone checking whether two lines are parallel (same slope) or perpendicular (slopes that are negative reciprocals of each other).
Given any two points on a line, the slope is fully determined — there's exactly one straight line through two distinct points, and exactly one slope that describes it.
How it’s calculated
Slope is 'rise over run': m = (y₂ − y₁) / (x₂ − x₁). The numerator (rise) is how far the line moves vertically between the two points; the denominator (run) is how far it moves horizontally. Dividing one by the other gives a single number that describes the line's steepness and direction.
The sign tells you the direction: positive slope means the line climbs left to right, negative means it falls, zero means it's perfectly flat (horizontal), and an undefined slope (division by zero, when both points share the same x-value) means the line is perfectly vertical.
Once you have the slope, the full line equation follows from a single point: y = mx + b, where b (the y-intercept) is found by plugging one of the known points back into that equation and solving for b.
Frequently asked questions
How do you find the slope between two points?
Subtract the y-values to get the rise, subtract the x-values (in the same order) to get the run, then divide: m = (y₂ − y₁) / (x₂ − x₁).
What does a negative slope mean?
The line falls as it moves left to right — for every step you take to the right along the x-axis, the y-value decreases rather than increases.
What's the difference between a zero slope and an undefined slope?
A zero slope is a perfectly horizontal line (no rise at all, just run). An undefined slope is a perfectly vertical line — there's no run (Δx = 0), and dividing by zero has no defined value.
How do I know if two lines are parallel or perpendicular from their slopes?
Parallel lines share the exact same slope. Perpendicular lines have slopes that are negative reciprocals of each other — for example, a slope of 2 and a slope of −1/2 meet at a right angle.
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