Let first put the equation of the first line in the form of slope intercept
[tex]\begin{gathered} 6x+3y=-9\rightarrow \\ y=\frac{-9-6x}{3}=-3-2x \end{gathered}[/tex]So it's slope is -2, so the new slope is
[tex]m=-\frac{1}{-2}=\frac{1}{2}[/tex]Having the slope, we have that
[tex]\begin{gathered} y-2=\frac{1}{2}(x+2)=\frac{1}{2}x+1 \\ y=\frac{1}{2}x+1+2=\frac{1}{2}x+3 \end{gathered}[/tex]so the equation is
[tex]y=\frac{1}{2}x+3[/tex]