Answer
$a.$
A line parallel to the given line has slope $m= -\displaystyle \frac{3}{2}.$
$b.$
A line perpendicular to the given line has slope $m=\displaystyle \frac{2}{3}$
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+2y=6 \qquad$ ... solve for y
$ 2y=-3x+6\qquad$ ... /$\div 2$
$y= -\displaystyle \frac{3}{2}x+3 \quad$ The given line has slope $m= -\displaystyle \frac{3}{2}$.
$ -\displaystyle \frac{3}{2}\cdot(\frac{2}{3})=-1$
$a.$
A line parallel to the given line has slope $m= -\displaystyle \frac{3}{2}.$
$b.$
A line perpendicular to the given line has slope $m=\displaystyle \frac{2}{3}$
