Point-Slope Form Calculator
Write the equation of a line as y − y₁ = m(x − x₁) from two points, a point and slope, the slope and intercept, or standard form.
Change the values and press Calculate to work out your own figures.
From two points
Enter two points on the line.
Show the working
- m = (y₂ − y₁) ÷ (x₂ − x₁) = (5 − 4) ÷ (7 − 3)
- Slope m = 1/4
- y-intercept b = 13/4
From a point and the slope
Enter a point and the slope.
Show the working
- Through (3, 4) with slope 1/4
- Slope m = 1/4
- y-intercept b = 13/4
From the slope and y-intercept
Enter the slope and the y-intercept.
Show the working
- Slope 2, crossing the y-axis at -3
- Slope m = 2
- y-intercept b = -3
From Ax + By = C
Enter A, B and C.
Show the working
- 2x + 3y = 6
- Slope m = -2/3
- y-intercept b = 2
How to use it
Enter two points on the line. Enter a point and the slope. Enter the slope and the y-intercept. Enter A, B and C.
Enter coordinates as whole numbers, decimals or fractions (3/4). Show the working gives the formula with your numbers.
Key facts
y − y₁ = m(x − x₁)
Which point?
Any point on the line works; the calculator uses the point you gave (or the y-intercept).
Questions
Through (3, 4) with slope 1/4?
y − 4 = 1/4(x − 3).
Through (−1, 2) with slope −3?
y − 2 = -3(x + 1).
Formulas
y − y₁ = m(x − x₁)
Sources
Limitations
- Vectors have two or three components (leave z blank for 2-D).
- Earth distances assume the WGS 84 ellipsoid (sea level).