Question

Identify an equation in point-slope form for the line perpendicular to

Answer 1

Given:

Equation of line is $y=\dfrac{1}{4}x-7$.

The perpendicular line passes through (-2,-6).

To find:

The point slope form of perpendicular line.

Solution:

We have,

$y=\dfrac{1}{4}x-7$

On comparing this equation with $y=mx+b$, we get

$m=\dfrac{1}{4}$

Slope of given line is $\dfrac{1}{4}$.

Product of slopes of two perpendicular of the lines is -1.

So, $Slope\times \dfrac{1}{4}=-1$

$Slope=-4$

Slope of required line is -4 and it passes through (-2,-6). So, the point slope form is

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

where, m is slope.

$y-(-6)=-4(x-(-2))$

$y+6=-4(x+2)$

Therefore, the correct option is A.