Question

Find the equation for the line that passes through the point (−2,0), and that is perpendicular to the line with the equation 2/3x+y=−14/3.

Answer 1

y = 3/2 x + 3

Explanation:

2/3 x + y = -14/3

y = -2/3 x − 14/3

The slope of this line is -2/3. So the perpendicular slope is the opposite of the inverse:

m = -1 / (-2/3)

m = 3/2

We know the slope of the line and a point on the line, so using point-slope form:

y − 0 = 3/2 (x − (-2))

Simplifying into slope-intercept form:

y = 3/2 (x + 2)

y = 3/2 x + 3