Equation of a Line Calculator
Find the equation of a line in standard, slope-intercept and point-slope form from two points, a point and slope, the slope and intercept, or Ax + By = C.
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
Ax + By = C; y = mx + b; y − y₁ = m(x − x₁)
Three forms
Standard form uses whole numbers; slope-intercept form shows the slope and where the line crosses the y-axis; point-slope form keeps a known point in view.
Questions
What line goes through (3, 4) and (7, 5)?
x − 4y = -13, or y = 1/4x + 13/4.
What about a vertical line?
It is written x = c; it has no slope-intercept form.
Formulas
Ax + By = C; y = mx + b; 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).