Point slope form

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

y - y1 = m(x - x1),

where m is the slope of the line, (x1, y1) 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.


The reason we use x and y instead of x2 and y2 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) (x1, y1)
(-5, 3) (3, 7)

See also slope.