Enter two points
Example data table
| Point 1 (x1, y1) | Point 2 (x2, y2) | Δx | Δy | Slope | Equation |
|---|---|---|---|---|---|
| (2, 3) | (8, 15) | 6 | 12 | 2 | y = 2x - 1 |
| (4, -2) | (4, 6) | 0 | 8 | Undefined | x = 4 |
Values are shown for learning and quick validation.
Formula used
- Δx = x2 − x1 and Δy = y2 − y1
- m = Δy / Δx (slope), when Δx ≠ 0
- b = y1 − m·x1 (y-intercept), when slope exists
- θ = arctan(m) (angle from the x-axis)
- distance = √((Δx)² + (Δy)²) and midpoint ((x1+x2)/2, (y1+y2)/2)
If Δx = 0, the line is vertical and the slope is undefined.
How to use this calculator
- Enter x1, y1, x2, and y2.
- Choose decimal places and a maximum denominator for fraction output.
- Enable worked steps or extra metrics, if needed.
- Click Calculate slope to view results above the form.
- Use the download buttons to export your latest result.
FAQs
1) What does slope measure?
Slope measures how much y changes for each unit change in x. A larger absolute slope means a steeper line. Positive values rise left-to-right, negative values fall, and zero means a horizontal line.
2) Why is the slope undefined for a vertical line?
A vertical line has Δx = 0, so the formula m = Δy/Δx would divide by zero. Division by zero is not defined, so the slope cannot be represented as a real number.
3) Can I enter fractions like 3/8?
Yes. Enter values as decimals or simple fractions in the form a/b. The calculator converts them to numeric values, then computes slope and related outputs from the two points.
4) What is the angle output?
The angle is θ = arctan(m), measured from the x-axis. It is shown in degrees and radians. Vertical lines show ±90° because their direction is straight up or down.
5) How is the line equation computed?
When slope exists, the calculator finds b using b = y1 − m·x1. It then displays y = mx + b and also shows a point-slope version that uses your first point.
6) What does “grade percent” mean?
Grade percent is slope multiplied by 100. For example, a slope of 0.12 corresponds to a 12% grade. It is common in roads, ramps, and basic engineering contexts.
7) How accurate is the fraction display?
The fraction is an approximation of the decimal slope using a maximum denominator you choose. Increasing the maximum can produce a closer match, but may create large numerators and denominators.
8) What if both points are the same?
If both points match exactly, there is no unique line through them. The calculator reports coincident points and still shows Δx, Δy, distance, and the midpoint for reference.
Note: This tool is for learning and general calculations. For precision-critical work, confirm units, rounding, and assumptions.