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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.
Slope Calculator: step-by-step worked example
The line through A(1, 2) and B(4, 11).
- x₁
- 1
- y₁
- 2
- x₂
- 4
- y₂
- 11
- 1
Rise
Δy = y₂ − y₁
11 − 2 = 9
- 2
Run
Δx = x₂ − x₁
4 − 1 = 3
- 3
Slope
m = Δy ÷ Δx
9 ÷ 3 = 3
- 4
y-intercept
b = y₁ − m × x₁
2 − 3 × 1 = -1
- 5
Line equation and angle
y = mx + b · α = arctan(m)
= y = 3x − 1 · α = 71.57°
- y = 3x − 1:-1 → 14
Good to know: A positive slope rises to the right, a negative one falls; m = 0 is horizontal. If x₁ = x₂ the line is vertical and the slope is undefined. Swapping the points does not change the result.
Slope Calculator — how it works
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.
Slope, angle and line equation from two points
| Points | Slope | Angle | Equation |
|---|---|---|---|
| (0, 0) → (1, 1) | 1 | 45° | y = x |
| (0, 0) → (1, 2) | 2 | 63.4° | y = 2x |
| (0, 0) → (2, 1) | 0.5 | 26.6° | y = 0.5x |
| (1, 1) → (4, 3) | 0.667 | 33.7° | y = 0.666667x + 0.333333 |
| (2, 3) → (5, 11) | 2.667 | 69.4° | y = 2.666667x − 2.333333 |
| (0, 5) → (5, 0) | -1 | -45° | y = -x + 5 |
| (-2, -1) → (2, 3) | 1 | 45° | y = x + 1 |
| (1, 2) → (3, 2) | 0 | 0° | y = 0x + 2 |
Frequently asked questions
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°.
Related guides
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
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How we calculate and our accuracy policy →
Results are for information only. For official matters the relevant authority's calculation prevails.
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