if the line is perpendicular to:
[tex]y=3x+3[/tex]then we know that the slope will be the negative reciproc of 3 so:
[tex]m=-\frac{1}{3}[/tex]Now we use this equation to find the intercept in the y axis:
[tex]m=\frac{y-y_1}{x-x_1}[/tex]we replace the slope, the coordinate (3,-2) and x=0 so:
[tex]\begin{gathered} -\frac{1}{3}=\frac{y-(-2)}{0-3} \\ \frac{3}{3}=y+2 \\ 1-2=y \\ -1=y \end{gathered}[/tex]So the final equation will be:
[tex]y=-\frac{1}{3}x-1[/tex]