# Point slope form

Point-slope form is a way to write linear equations given by the equation:

y - y_{1} = m(x - x_{1}),

where m is the slope of the line, (x_{1}, y_{1}) is a point on the line, and (x, y) is any other point on the line.

Notice that point-slope form is more or less a rearranged form of the slope formula.

Example

The reason we use x and y instead of x_{2} and y_{2} is that in the slope formula, we were solving for m by using two points, but hwen we are using point-slope form, we are writing a linear equation, so x and y need to be there in the final equation.

Given two points, you can write an equation in point-slope form:

(x, y) | (x_{1}, y_{1}) |

(-5, 3) | (3, 7) |

See also slope.