#### Answer

Parallel.

#### Work Step by Step

To determine if the lines are parallel, we compare their slopes.
The line $y=-\frac{1}{3}x-1$ has a slope $-\frac{1}{3}$.
We need to find the slope of the line $9y+3x+3=0$:
$9y+3x+3=0$
$9y=-3x-3$
$y=- \frac{1}{3}x-\frac{1}{3}$
So this line has a slope of $-\frac{1}{3}$.
Since the slopes are the same, the lines are parallel.