Use point-slope form to write an equation of the line passing through the two given points...

Use point-slope form to write an equation of the line passing through the two given points. Then write the equation in slope-intercept form. See Example.

EXAMPLE 2 Write an equation of the line passing through (-5, 4) and (8, -6).

Strategy We will use the point-slope form, y — y1 = m(x — x1), to write the equation of the line.

WHY Since we know two points on the line, we can calculate the slope of the line and solve the problem using the method of Example 1.

Solution

First we find the slope of the line.

Since the line passes through (-5, 4) and (8, -6), we can choose either point and substitute its coordinates into the point-slope form. If we choose (-5, 4), we substitute -5 for x1, 4 for y1, and for m and proceed as follows.

y — y1 = m(x — x1)This is the point-slope form.

The equation of the line is .

 (4,0), (6, −8)