How to use it
- Type the two points. Each coordinate can be a whole number, a decimal (2.75), a fraction (−3/4) or a mixed number (2 1/2).
- The slope appears at once as an exact fraction and as a decimal, with the line’s equation in slope-intercept, point-slope and standard form, its intercepts, the distance between the points, the midpoint and the angle the line makes with the x-axis.
- Every equation has a Copy button, and the steps under the results show the rise, the run and the y-intercept worked out.
The formula, worked through
Slope is rise over run: m = (y2 − y1) ÷ (x2 − x1). For the points (−1, 2) and (3, 5), the rise is 5 − 2 = 3 and the run is 3 − (−1) = 4, so m = 3/4: the line climbs 3 units for every 4 to the right. The y-intercept follows from b = y1 − m·x1 = 2 − (3/4)(−1) = 11/4. The calculator writes the same line three ways:
| Form | For (−1, 2) and (3, 5) | Useful for |
|---|---|---|
| Slope-intercept, y = mx + b | y = (3/4)x + 11/4 | reading the slope and where the line crosses the y-axis |
| Point-slope, y − y1 = m(x − x1) | y − 2 = (3/4)(x + 1) | writing a line straight from one point and its slope |
| Standard, Ax + By = C | 3x − 4y = −11 | whole-number coefficients, systems of equations, and vertical lines |
Standard form is written with whole numbers that share no common factor and a positive x coefficient (or a positive y coefficient when there is no x term), the convention most textbooks use, so 6x − 8y = −22 and −3x + 4y = 11 both come out as 3x − 4y = −11.
Vertical and horizontal lines
When both points have the same x-coordinate, the run is zero and the slope is undefined: you cannot divide by zero. The line is vertical, its equation is x = (that x-coordinate), it has no y-intercept and it cannot be written in slope-intercept form. When both points have the same y-coordinate, the rise is zero, so the slope is 0 and the line is horizontal: y = (that y-coordinate). A slope of 0 and an undefined slope are different things, a common mix-up on tests.
Why exact fractions
Decimal calculators turn the slope between (0, 0) and (3, 1) into 0.3333333333 and then build the intercept and the equation from the rounded value, which is how answers end up off in the last digit. This calculator reads what you type exactly (0.1 is 1/10, not the nearest binary number), does all the arithmetic on whole-number fractions, and reduces at the end. The distance between the points is shown in simplest radical form, such as 6√5 for (2, −3) and (−4, 9), and as a decimal.
What we tested
On October 15, 2026 we ran the page’s own functions on 3,000 random pairs of points written as whole numbers, decimals, fractions and mixed numbers, and checked every answer with the SymPy computer-algebra library: slope, y-intercept, standard-form coefficients (both points satisfy them, no common factor, sign rule), distance (equal to the exact square root, with nothing square left under the radical), midpoint and angle were all correct in every case, including 133 vertical and 135 horizontal lines; the same point twice and unreadable input gave a message instead of an answer. Each equation the page displays was read back by SymPy and passed through both points. In Chromium: (−1, 2) and (3, 5) showed slope 3/4 (0.75), y = (3/4)x + 11/4, y − 2 = (3/4)(x + 1), 3x − 4y = −11, distance 5, midpoint (1, 7/2) and 36.8699°; fractions and a mixed number gave 16/9 and a distance of (1/12)√337; a vertical line showed an undefined slope and x = 4, a horizontal one slope 0 and no x-intercept; the same point twice and a typo each showed a message; Copy put y = -2x + 1 on the clipboard; the points survived a reload; the page fitted a 390 px phone with no errors. We also checked the check: removing the standard-form sign rule made 1,486 of the cases fail.
Sources
Checked on .
Frequently Asked Questions
Built by Derek Giordano · Part of Ultimate Design Tools