Question

Pls help me out!! lol

Answer 1

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

Explanation:

The equation of the line is perpendicular to the line $y-12=2 x-8$ and that passes through the point $(2,3)$

We need to determine the equation of the line.

First, let us determine the slope of the equation.

Since, the equation is perpendicular to the line $y-12=2 x-8$, the slope is $m=2$

Since, the lines are perpendicular, we have,

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

Now, we shall substitute the slope $m=-\frac{1}{2}$ and the point $(2,3)$ in the slope - point formula, we have,

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

$y-3=-\frac{1}{2} (x-2)$

$y-3=-\frac{1}{2} x+1$

Hence, writing this equation in slope - intercept form, we have,

$y=-\frac{1}{2} x+1+3$

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

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

Therefore, Option D is the correct answer.