Equation of a Line Calculator
Find line equations in all forms from various inputs
Point 1
Point 2
Step-by-Step Solution
Forms of Linear Equations
Slope-Intercept Form: y = mx + b
Shows slope (m) and y-intercept (b) directly. Best for graphing and understanding rate of change.
Point-Slope Form: y - y₁ = m(x - x₁)
Uses a point (x₁, y₁) and slope (m). Ideal when you know a point and the slope.
Standard Form: Ax + By = C
Integer coefficients with A positive. Useful for systems of equations and finding intercepts quickly.
Intercept Form: x/a + y/b = 1
Shows x-intercept (a) and y-intercept (b) directly. Perfect when intercepts are known.
Frequently Asked Questions
Which form should I use?
It depends on what you know and need. Slope-intercept is most common, point-slope is best when you have a point and slope, standard form is good for integer work, and intercept form is perfect when you know both intercepts.
How do I convert between forms?
Use algebra to rearrange. For example, from y = mx + b to standard form, subtract mx from both sides to get -mx + y = b.
Can all lines be written in all forms?
Almost! Vertical lines (x = c) can't be written in slope-intercept form. Lines through the origin can't use intercept form.
What if I only know two points?
First calculate the slope, then use either point with the slope to write the equation in any form you need.
Why use standard form?
Standard form is preferred in some contexts because it uses integers and treats x and y symmetrically, making it easier for certain calculations.
What's the easiest form for graphing?
Slope-intercept form (y = mx + b) is easiest. Start at the y-intercept and use the slope to find other points.