How do I find a line equation from two points?

First find slope: m = (y₂ - y₁) / (x₂ - x₁). Then use point-slope form: y - y₁ = m(x - x₁). Rearrange to y = mx + b to find b-intercept.

What is point-slope form?

y - y₁ = m(x - x₁) where (x₁, y₁) is a known point and m is slope. Convert to slope-intercept by solving for y.

Substitute m and either point into y = mx + b, then solve for b.

The line is vertical (undefined slope). Equation is x = constant.

Cannot determine a unique line. Need two distinct points.

Math

Find line equation y = mx + b from two coordinate points.

Point 1: x₁

Point 1: y₁

Point 2: x₂

Point 2: y₂

Line Equation

Slope (m)—

Y-intercept (b)—

Equation—

First find slope: m = (y₂ - y₁) / (x₂ - x₁). Then use point-slope form: y - y₁ = m(x - x₁). Rearrange to y = mx + b to find b-intercept.
y - y₁ = m(x - x₁) where (x₁, y₁) is a known point and m is slope. Convert to slope-intercept by solving for y.
Substitute m and either point into y = mx + b, then solve for b.
The line is vertical (undefined slope). Equation is x = constant.
Cannot determine a unique line. Need two distinct points.