Answer
Line $b$ is perpendicular to line $a$.
Work Step by Step
Line $a:$
Let $(x_1,y_1)=(-2,2)$ and $(x_2,y_2)=(2,1)$
Slope
$\Rightarrow m_a=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m_a=\frac{1-2}{2-(-2)}$
Simplify.
$\Rightarrow m_a=\frac{-1}{2+2}$
$\Rightarrow m_a=-\frac{1}{4}$
Line $b:$
Let $(x_1,y_1)=(1,-8)$ and $(x_2,y_2)=(3,0)$
Slope
$\Rightarrow m_b=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m_b=\frac{0-(-8)}{3-1}$
Simplify.
$\Rightarrow m_b=\frac{8}{2}$
$\Rightarrow m_b=4$
Line $c:$
Let $(x_1,y_1)=(-4,-3)$ and $(x_2,y_2)=(0,-2)$
Slope
$\Rightarrow m_c=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m_c=\frac{-2-(-3)}{0-(-4)}$
Simplify.
$\Rightarrow m_c=\frac{-2+3}{0+4}$
$\Rightarrow m_c=\frac{1}{4}$
Line $b$ has a slope of $4$, the negative reciprocal of $-\frac{1}{4}$, so it is perpendicular to line $a$.
