Slope Through (0, 0) and (5, 5)
The slope, incline angle, distance, and line equation for this pair of points. Adjust any coordinate below to solve your own.
Slope
1
The line through (0, 0) and (5, 5) has a slope of 1 (rise 5 over run 5), an incline angle of about 45°, and the equation y = 1x + 0.
Incline Angle
45°
Distance Between Points
7.0711
Line Equation
y = 1x + 0
What Is Slope?
Slope is a number that measures the steepness and direction of a line — how much it rises or falls (the "rise") for every unit it moves horizontally (the "run"). A positive slope means the line rises left to right; a negative slope means it falls; a slope of zero means the line is perfectly horizontal; and a vertical line has an undefined slope, since it has zero horizontal run.
Slope is one of the most fundamental concepts in algebra and calculus, forming the basis for linear equations, rates of change, and — in calculus — the derivative, which generalizes slope to curves.
The line through your two points
How Is Slope Calculated?
Given two points (x₁, y₁) and (x₂, y₂), slope is the change in y divided by the change in x — commonly remembered as "rise over run." The same value also equals the tangent of the line's angle of incline from horizontal.
Reading the Sign and Value of a Slope
A slope of 1 means the line rises exactly as much as it runs (a 45° angle). A slope of 2 means it rises twice as fast as it runs — steeper than 45°. A slope between 0 and 1 (like 0.5) means the line rises more gradually than 45°. Negative slopes mirror this behavior in the downward direction.
Vertical and Horizontal Lines
A horizontal line has a slope of exactly zero, since y never changes no matter how far x moves. A vertical line has an undefined slope — the formula divides by zero, since x never changes — which is why this calculator reports "undefined" rather than a number for that case.
From Slope to a Full Line Equation
Once you know the slope and one point, the slope-intercept form y = mx + b is fully determined by solving for b (the y-intercept) using either known point — this calculator reports that full equation alongside the raw slope value.
Example — Your Current Inputs
The line through (0, 0) and (5, 5) has a slope of 1 (rise 5 over run 5), an incline angle of about 45°, and the equation y = 1x + 0.
Additional Example — A Wheelchair Ramp
A wheelchair ramp rising 1 foot over a 12-foot run has a slope of 1/12 ≈ 0.083 — the maximum slope generally permitted under ADA accessibility guidelines, corresponding to an incline angle of about 4.8°.
About These Parameters
- Point 1 (x₁, y₁) and Point 2 (x₂, y₂)
- Any two distinct coordinate points on the line. The order doesn't affect the slope value — swapping the two points flips the sign of both the rise and the run, leaving the ratio unchanged.
Frequently Asked Questions
What does a negative slope mean?
A negative slope means the line falls as it moves left to right — for every unit increase in x, y decreases by the absolute value of the slope.
Why is a vertical line's slope undefined instead of infinite?
Division by zero is undefined in standard arithmetic, not equal to infinity — so mathematically, "undefined" is the precise term, even though the line does become arbitrarily steep as it approaches vertical.
How is slope related to percent grade?
Percent grade, used for roads and ramps, is simply the slope expressed as a percentage — a slope of 0.05 is a 5% grade, meaning 5 feet of rise for every 100 feet of horizontal run.