Equation of a Line Calculator
This calculator finds the equation of a line given different types of input: two points, a point and slope, or slope and y-intercept. It displays the equation in slope-intercept form (y = mx + b), standard form (ax + by = c), and point-slope form.
Forms of line equations
Slope-intercept: y = mx + b
Point-slope: y - y1 = m(x - x1)
Standard: ax + by = c
From two points: m = (y2-y1)/(x2-x1)
Line equations: frequently asked questions
What are the different forms of a line equation?
Slope-intercept (y = mx + b), point-slope (y - y1 = m(x - x1)), and standard form (ax + by = c) are the most common forms.
When should I use each form?
Use slope-intercept to quickly identify slope and y-intercept. Use point-slope when you know a point and slope. Use standard form for general purposes or when the line has no y-intercept.
How do I convert between forms?
Algebraically rearrange the equation: expand, collect terms, isolate y, or convert to standard form by multiplying and collecting.
Can every line be written in all three forms?
Slope-intercept form cannot represent vertical lines (undefined slope). Standard and point-slope forms can represent all lines.
What is the formula for standard form?
Standard form is ax + by = c, where a, b, c are integers and a is typically positive.
Methodology
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.