Point-Slope Form for the Equation of a Line

Example

Find the equation of the line that passes through the points (-2, 7) and (6, 3). Write your answer in point-slope form.

Solution

To find the equation in point-slope form, we first find m, the slope of the line.

Let (x1, y1) = (-2, 7) and (x2, y2) = (6, 3).	m
Substitute the values in the slope formula.
Simplify.
Reduce.
The slope of the line is . Now that we have the slope and a point, we can use the point-slope form to find the equation of the line.	y - y1	= m(x - x1)
Substitute for m. We can substitute either given point for (x1, y1). Let’s use (6, 3).	y - y1
Therefore, substitute 6 for x1 and 3 for y1.	y - 3

The point-slope form of the equation of the line that passes through (-2, 7) and (6, 3) is

Note:

If we had used the other point, (-2, 7), we would have obtained:

This equation is equivalent to