Enter values and select Calculate.
Calculated result
Calculation steps
Slope formula
m = (y₂ − y₁) / (x₂ − x₁). The numerator is the rise and the denominator is the run.
How to find slope between two points
- Subtract the first y-coordinate from the second to find the rise.
- Subtract the first x-coordinate from the second to find the run.
- Divide rise by run and reduce the fraction when possible.
Positive, negative, zero and undefined slope
- A positive slope rises from left to right.
- A negative slope falls from left to right.
- A horizontal line has zero slope because its rise is 0.
- A vertical line has undefined slope because its run is 0.
Slope example
m = (y₂ − y₁) / (x₂ − x₁). A zero run produces an undefined vertical slope; a zero rise with nonzero run produces slope 0.
For (1, 2) and (3, 6), rise = 6 − 2 = 4 and run = 3 − 1 = 2, so m = 4/2 = 2.
Calculations use full internal precision and trim insignificant trailing zeros for display. Confirm any rounding rule required by a course, workplace, publication, or technical standard.
How to use it
Enter x₁ and y₁ for the first point.
Enter x₂ and y₂ for a distinct second point.
Calculate and review the signed rise and run.
Use the line-form output only when it matches the coordinate convention required for your work.
Vertical, horizontal, and identical points
When x₁ = x₂ but the y-values differ, the line is vertical and its slope is undefined; the equation is x = constant.
When y₁ = y₂ and the x-values differ, the line is horizontal and its slope is 0.
Two identical points do not determine a unique line, so the calculator returns a validation message rather than calling the line vertical.
Slope-intercept form
For a finite slope, point-slope form is shown as y − y₁ = m(x − x₁).
Slope-intercept form uses b = y₁ − mx₁ and is shown as y = mx + b.
Integer rise and run are reduced by their greatest common divisor for an exact fractional slope.
Methodology and limits
This deterministic calculator uses the formula shown above and strict finite-number parsing. It does not evaluate expressions, execute entered text, call a remote calculation service, or claim to replace instruction or professional review.