Answer
Line $c$ has a slope of $-\frac{2}{7}$, the negative reciprocal of $\frac{7}{2}$, so it is perpendicular to line $b$.
Work Step by Step
Line $a:$
$\Rightarrow 2x-7y=14$.
Slope intercept form is
$\Rightarrow y=\frac{2}{7}x-2$.
Slope is $m_a=\frac{2}{7}$
Line $b:$
$\Rightarrow y=\frac{7}{2}x-8$.
Slope is $m_b=\frac{7}{2}$
Line $c:$
$\Rightarrow 2x+7y=-21$.
Slope intercept form is
$\Rightarrow y=-\frac{2}{7}x-3$.
Slope is $m_c=-\frac{2}{7}$
Line $c$ has a slope of $-\frac{2}{7}$, the negative reciprocal of $\frac{7}{2}$, so it is perpendicular to line $b$.
