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Sagot :
(a)
The given equation of a line is,
[tex]3x+2y=-3\text{ ---(1)}[/tex]The general equation of a straight line is given by,
[tex]y=mx+c\text{ }---(2)[/tex]Here, m is the slope of the line and c is the y intercept.
Rewrite equation (1) into the form of equation (2).
[tex]\begin{gathered} 2y=-3x-3 \\ y=\frac{-3}{2}x-\frac{3}{2}\text{ ---(3)} \end{gathered}[/tex]Comparing equations (1) and (3), we get the slope of the line m=-3/2.
Two parallel lines has the same slope. So, the slope of a line parallel to the line 3x+2y=-3 with slope m=-3/2 is -3/2.
(b)
The slope of a line perpendicular to the line with slope m=-3/2 is,
[tex]M=\frac{-1}{m}=\frac{-1}{-\frac{3}{2}}=\frac{2}{3}[/tex]Therefore, the slope of a line perpendicular to 3x+2y=-3 with slope m=-3/2 is 2/3.
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