Enter the coordinates of two points and this calculator gives you the slope of the line through them, plus the y-intercept, the full equation y = mx + b, and the angle of incline in degrees.
How the slope calculator works
Slope measures how steep a line is: how much it rises (or falls) for every unit it moves to the right. Given two points, the calculator divides the change in y by the change in x — the classic rise over run. From the slope it then back-solves the y-intercept, writes out the full line equation, and converts the slope to an angle in degrees.
The formula
m = (y₂ − y₁) ÷ (x₂ − x₁)
m is the slope, and (x₁, y₁) and (x₂, y₂) are your two points. The y-intercept follows as b = y₁ − m·x₁, and the angle of incline is arctan(m).
Worked example
Take the points (2, 3) and (6, 11):
m = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2
b = 3 − 2 × 2 = −1, so the line is y = 2x − 1, climbing at an angle of arctan(2) ≈ 63.43°. In plain terms: for every step right, the line rises two.
The one mistake everyone makes
Mixing up the subtraction order. It doesn't matter which point you call "point 1" — but you must subtract in the same order on top and bottom. (11 − 3)/(6 − 2) and (3 − 11)/(2 − 6) both give 2, but (11 − 3)/(2 − 6) gives −2 and silently flips your line upside down. If your slope's sign surprises you, check the order first. And remember the two special cases: same y-values means slope 0 (horizontal), same x-values means the slope is undefined (vertical) — not zero.
Frequently asked questions
How do I find the slope between two points?
Subtract the y-coordinates, subtract the x-coordinates, and divide: slope = (y2 − y1) ÷ (x2 − x1). This is the famous "rise over run" — how much the line goes up (or down) for every unit it moves to the right.
What does an undefined slope mean?
If both points have the same x-coordinate, the line is perfectly vertical and the run is zero. Dividing by zero is undefined, so vertical lines have no slope. They're written as x = a constant instead of y = mx + b.
What does a slope of 0 mean?
A slope of 0 means the line is perfectly horizontal — the y-value never changes no matter how far you travel along x. Its equation is simply y = b, where b is the shared y-coordinate of every point on the line.
How do I find the y-intercept from two points?
First compute the slope m, then plug either point into b = y − m·x. The y-intercept is where the line crosses the y-axis, i.e. the value of y when x = 0. This calculator does both steps for you automatically.
How is slope related to the angle of a line?
The slope is the tangent of the line's angle with the horizontal axis, so angle = arctan(slope). A slope of 1 is a 45° incline, a slope of 2 is about 63.4°, and negative slopes give negative angles (the line goes downhill left to right).