ANSWER
[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]
EXPLANATION
The given line is
[tex]y = 3x + 3[/tex]
The given point is
[tex](-1,-1)[/tex]
The slope of the given line is
[tex]m = 3[/tex]
We found this by comparing
[tex]y = 3x + 3[/tex]
to
[tex]y = mx + b[/tex]
If two lines are perpendicular, then one is the negative reciprocal of the other.
Hence the slope of the required line is
[tex] - \frac{1}{3} [/tex]
Using the point-slope formula or otherwise, we can find the required equation.
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the slope and point to get:
[tex]y + 1 = - \frac{1}{3} (x + 1)[/tex]
[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]
