To find the slope intercept form, solve the equation for y.
[tex]\begin{gathered} 3y=2x+9 \\ y=\frac{2x+9}{3} \\ y=\frac{2}{3}x+\frac{9}{3} \\ y=\frac{2}{3}x+3 \end{gathered}[/tex]Solve the equation for x:
[tex]\begin{gathered} 3y=2x+9 \\ 2x+9=3y \\ 2x=3y-9 \\ x=\frac{3y-9}{2} \\ x=\frac{3}{2}y-\frac{9}{2} \end{gathered}[/tex]