Answer
$a.$
A line parallel to the given line has slope $m= \displaystyle \frac{3}{4}.$
$b.$
A line perpendicular to the given line has slope $m= -\displaystyle \frac{4}{3}$
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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Read the slope from $y=mx+b$
$ 3x-4y=-7 \qquad$ ... solve for y
$-4y=-3x-7 \qquad$ ... /$\div(-4)$
$y= \displaystyle \frac{3}{4}x+\frac{7}{4} \quad$ The given line has slope $m= \displaystyle \frac{3}{4}$.
$ \displaystyle \frac{3}{4}\cdot(-\frac{4}{3})=-1$
$a.$
A line parallel to the given line has slope $m= \displaystyle \frac{3}{4}.$
$b.$
A line perpendicular to the given line has slope $m= -\displaystyle \frac{4}{3}$
