Answer
$a.$
A line parallel to the given line has slope $m= \displaystyle \frac{2}{3}.$
$b.$
A line perpendicular to the given line has slope $m= -\displaystyle \frac{3}{2}$
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 $y=mx+b$
$ 2x-3y=5 \qquad$ ... solve for y
$-3y=-2x+5 \qquad$ ... /$\div(-3)$
$y= \displaystyle \frac{2}{3}x+\frac{5}{3} \quad$ The given line has slope $m= \displaystyle \frac{2}{3}$.
$ \displaystyle \frac{2}{3}\cdot(-\frac{3}{2})=-1$
$a.$
A line parallel to the given line has slope $m= \displaystyle \frac{2}{3}.$
$b.$
A line perpendicular to the given line has slope $m= -\displaystyle \frac{3}{2}$
