Use the point-slope form of a line:
y−y1=m(x−x1)

Substitute \(\displaystyle{m}=\frac{{3}}{{2}}\) and (x1,y1)=(−3,−1): \(\displaystyle{y}-{\left(-{1}\right)}=\frac{{3}}{{2}}{\left({x}-{\left(-{3}\right)}\right)}\)

\(\displaystyle{y}+{1}=\frac{{3}}{{2}}{x}+\frac{{9}}{{2}}\)

The standard form of a line is Ax+By=C. Multiply both sides by 2:

PSK2y+2=3x+9

Rearranging,

−7=3x−2y

or

3x−2y=−7

Substitute \(\displaystyle{m}=\frac{{3}}{{2}}\) and (x1,y1)=(−3,−1): \(\displaystyle{y}-{\left(-{1}\right)}=\frac{{3}}{{2}}{\left({x}-{\left(-{3}\right)}\right)}\)

\(\displaystyle{y}+{1}=\frac{{3}}{{2}}{x}+\frac{{9}}{{2}}\)

The standard form of a line is Ax+By=C. Multiply both sides by 2:

PSK2y+2=3x+9

Rearranging,

−7=3x−2y

or

3x−2y=−7