Answer
$a.$
A line parallel to the given line has slope $m=4.$
$b.$
A line perpendicular to the given line has slope $m=-\displaystyle \frac{1}{4}$
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 $y=mx+b$
$ 4x+y=7\qquad$ ... solve for y
$y= -4x+7$: $\quad$ The given line has slope $m=4$.
$4\displaystyle \cdot(-\frac{1}{4})=-1$
$a.$
A line parallel to the given line has slope $m=4.$
$b.$
A line perpendicular to the given line has slope $m=-\displaystyle \frac{1}{4}$
