✏️ Equation of a Line Calculator
Every straight line has an equation, and there are three standard ways to write it: slope-intercept (y = mx + b), point-slope (y − y₁ = m(x − x₁)) and standard form (Ax + By = C). Different starting information suits different forms, and converting between them is a daily algebra task.
Tell this calculator what you know — two points, one point and the slope, or the slope and y-intercept — and it produces all three forms, both intercepts and the angle of the line, with the line drawn on a graph.
How to use this calculator
Pick the form that matches your given information, fill in its fields, and read all three versions of the equation from the results.
- Choose what you know: two points, a point and slope, or slope and y-intercept.
- Fill in the fields for that choice (the other fields are ignored).
- Press Calculate.
- Read the slope-intercept, point-slope and standard forms, and check the line on the graph.
Equation of a Line Worked Example
Find the equation of the line through (1, 2) and (3, 8). The slope is m = (8 − 2)/(3 − 1) = 3. Using (1, 2) in point-slope form: y − 2 = 3(x − 1), which expands to y = 3x − 1 (so b = −1). In standard form that is 3x − y = 1. The line crosses the x-axis at x = 1/3 and rises at an angle of arctan(3) ≈ 71.6°. Those are the default values above.
Frequently asked questions
Which form of a line equation should I use?
Slope-intercept (y = mx + b) is best for graphing and reading off slope and intercept. Point-slope is the quickest to write when you know a point and the slope. Standard form (Ax + By = C) is the convention for systems of equations and many textbook answers. They all describe the same line.
How do I find the equation of a line from two points?
First compute the slope m = (y₂ − y₁)/(x₂ − x₁). Then take either point and write point-slope form y − y₁ = m(x − x₁), and rearrange if you want slope-intercept form. This calculator does all three forms in one step.
What is the equation of a vertical line?
A vertical line has no slope and no y-intercept, so it cannot be written as y = mx + b. Its equation is simply x = a, where a is the x-coordinate of every point on it — for example x = 3. Enter two points with the same x in this calculator and it returns exactly that.
Why does my standard form look different from the answer key?
Standard form is usually written with integer coefficients, A positive, and common factors divided out: 3x − y = 1 rather than 6x − 2y = 2. This calculator scales to integers and removes common factors automatically, so it should match the conventional form.