Question

Write a equation in slope intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (-3,2); x-2y=7 How do I solve it?

Answer 1

The perpendicular line would be y = -2x - 4

Explanation:

First we must solve the original equation for y.

x - 2y = 7

-2y = -x + 7

y = 1/2x - 7/2

In order to find the equation of this line, we first have to note that perpendicular lines have opposite and reciprocal slopes. Therefore, since the original line has a slope of 1/2, we know the new line will have a slope of -2. Now we can use that information along with the given point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 2 = -2(x + 3)

y - 2 = -2x - 6

y = -2x - 4