Answer
$a.$
A line parallel to the given line has slope $m=\displaystyle \frac{1}{4}.$
$b.$
A line perpendicular to the given line has slope $m=-4$
Work Step by Step
If two nonvertical lines are parallel, then they have the same slope.
If two nonvertical lines are perpendicular, then the product of their slopes is -1.
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Reading the slope from $y=mx+b$
$y= \displaystyle \frac{1}{4}x-5$: $\quad$ The given line has slope $m=\displaystyle \frac{1}{4}$.
$\displaystyle \frac{1}{4}\cdot(-4)=-1$
$a.$
A line parallel to the given line has slope $m=\displaystyle \frac{1}{4}.$
$b.$
A line perpendicular to the given line has slope $m=-4$
