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Give two points and this calculator finds the slope of the line through them — how steep it is and which way it tilts — along with the y-intercept, the full equation y = mx + b, the angle of incline, and the distance between the points.
How is it calculated?
Slope is rise over run
Slope (m) is the change in y divided by the change in x:
m = (y₂ − y₁) ÷ (x₂ − x₁)
| Slope | Meaning |
|---|---|
| Positive | Line rises left to right |
| Negative | Line falls left to right |
| Zero | Horizontal line |
| Undefined | Vertical line (x₁ = x₂) |
A vertical line has no slope — the run is zero, so the division is undefined.
From slope to the full line
Once you have the slope, the y-intercept (b) is where the line crosses the y-axis: b = y₁ − m·x₁. Together they give the slope-intercept equation y = mx + b. The angle of incline is arctan(m), and the straight-line distance between the points is √((x₂−x₁)² + (y₂−y₁)²) — the Pythagorean theorem again.
Worked example
For the points (1, 2) and (3, 6): the slope is (6 − 2) ÷ (3 − 1) = 4 ÷ 2 = 2. The y-intercept is 2 − 2×1 = 0, so the line is y = 2x. Its angle of incline is arctan(2) ≈ 63.4°, and the distance between the two points is √(2² + 4²) = √20 ≈ 4.47.
FAQ
How do I calculate the slope between two points?+
Divide the change in y by the change in x: m = (y₂ − y₁) ÷ (x₂ − x₁). For (1, 2) and (3, 6) that’s (6 − 2) ÷ (3 − 1) = 2. The tool also gives the y-intercept and full equation.
What does the slope tell me?+
How steep the line is and its direction. A positive slope rises from left to right, a negative one falls, zero is flat, and a larger absolute value is steeper. A slope of 2 means y increases by 2 for every 1 that x increases.
What is the y-intercept?+
The point where the line crosses the y-axis, i.e. the value of y when x = 0. It’s found with b = y₁ − m·x₁ and is the “b” in the slope-intercept equation y = mx + b.
Why is the slope sometimes undefined?+
When the two points share the same x value, the line is vertical and the run (x₂ − x₁) is zero. Dividing by zero is undefined, so a vertical line has no slope — the calculator flags this instead of returning a number.
How is the angle of the line found?+
By taking the arctangent of the slope: angle = arctan(m), in degrees. A slope of 1 is a 45° incline, a slope of 0 is horizontal (0°), and steeper slopes approach 90°.