Answer
Lines $b$ and $c$ have slopes of $3$, so they are parallel.
Line $a$ has a slope of $-\frac{1}{3}$, the negative reciprocal of $3$, so it is perpendicular to lines $b$ and $c$.
Work Step by Step
Line $a:$
$\Rightarrow 2x+6y=-3$.
Slope intercept form is
$\Rightarrow y=-\frac{1}{3}x-\frac{1}{2}$.
Slope is $m_a=-\frac{1}{3}$
Line $b:$
$\Rightarrow y=3x-8$.
Slope is $m_b=3$
Line $c:$
$\Rightarrow -6y+18x=9$.
Slope intercept form is
$\Rightarrow y=3x-\frac{3}{2}$.
Slope is $m_c=3$
Lines $b$ and $c$ have slopes of $3$, so they are parallel.
Line $a$ has a slope of $-\frac{1}{3}$, the negative reciprocal of $3$, so it is perpendicular to lines $b$ and $c$.
