Answer
Lines $a$ and $b$ have slopes of $\frac{4}{3}$, so they are parallel.
Line $c$ has a slope of $-\frac{3}{4}$, the negative reciprocal of $\frac{4}{3}$, so it is perpendicular to lines $a$ and $b$.
Work Step by Step
Line $a:$
$\Rightarrow 4x-3y=2$.
Slope intercept form is
$\Rightarrow y=\frac{4}{3}x-\frac{2}{3}$.
Slope is $m_a=\frac{4}{3}$
Line $b:$
$\Rightarrow y=\frac{4}{3}x+2$.
Slope is $m_b=\frac{4}{3}$
Line $c:$
$\Rightarrow 4y+3x=4$.
Slope intercept form is
$\Rightarrow y=-\frac{3}{4}x+1$.
Slope is $m_c=-\frac{3}{4}$
Lines $a$ and $b$ have slopes of $\frac{4}{3}$, so they are parallel.
Line $c$ has a slope of $-\frac{3}{4}$, the negative reciprocal of $\frac{4}{3}$, so it is perpendicular to lines $a$ and $b$.
