Answer
$a$ and $b$ are parallel.
Slopes are same for parallel lines. Slope of the line perpendicular to a line with slope $m$ is $-\frac{1}{m}$.
Since the slopes of line $a$ and $b$ are equal, line $a$ and line $b$ are parallel.
Work Step by Step
For line $a$, slope $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{0-1}{2-(-1)}=\frac{-1}{3}$
For line $b$, $m=\frac{4-5}{3-0}=\frac{-1}{3}$
For line $c$, $m=\frac{5-0}{2-0}=\frac{5}{2}$
Slopes are same for parallel lines. Slope of the line perpendicular to a line with slope $m$ is $-\frac{1}{m}$.
Since the slopes of line $a$ and $b$ are equal, line $a$ and line $b$ are parallel.
