Answer
(a) $y=-4x-16$
(b) $y=\frac{1}{4}x+1$
Work Step by Step
The given line passes through the points $(-3,3)$ and $(-2,-1)$.
$\text{Slope of the given line}=\frac{-1-3}{-2-(-3)}=\frac{-4}{1}=-4$.
The point given is $(x_{1},y_{1})=(-4,0)$.
(a) For parallel line, the slope is same.
Using point-slope form $y-y_{1}=m(x-x_{1})$, we have
$y-0=-4(x-(-4))$
Using distributive property, we get
$y=-4x-16$
An equation of the line that passes through the given point and is parallel to the given line is $y=-4x-16$.
(b) For perpendicular lines, the slopes are negative reciprocals.
$\implies m=-(\frac{1}{-4})=\frac{1}{4}$.
Using point-slope form, we have
$y-0=\frac{1}{4}(x-(-4))$
Using distributive property, we get
$y=\frac{1}{4}x+1$
An equation of the line that passes through the given point and is perpendicular to the given line is $y=\frac{1}{4}x+1$.
