Question

Find the equation of the line that is perpendicular to y = 2x + 8 and passes though the point (8, –8).

Answer 1

Option B: $y=-\frac{1}{2} x-4$ is the equation of the line.

Explanation:

Given that the equation of the line is perpendicular to $y = 2x + 8$ and passes through the point $(8,-8)$

We need to determine the equation of the line.

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

First, we shall find the value of m.

From the equation $y = 2x + 8$, the slope is 2.

Since, the lines are perpendicular, the slope is given by

$m=-\frac{1}{2}$

Thus, the slope is $m=-\frac{1}{2}$

Substituting the slope $m=-\frac{1}{2}$ and the point $(8,-8)$ in the formula $y-y_1=m(x-x_1)$, we get,

$y+8=-\frac{1}{2} (x-8)$

Simplifying, we get,

$y+8=-\frac{1}{2} x+4$

Subtracting both sides by 8, we get,

$y=-\frac{1}{2} x-4$

Thus, the equation of the line is $y=-\frac{1}{2} x-4$

Therefore, Option B is the correct answer.