1. **State the problem:** Determine if the point $(-2, -2)$ lies on the line given by the equation $$y = -\frac{1}{3}x + 9$$. 2. **Recall the formula:** The equation of the line is $$y = -\frac{1}{3}x + 9$$. To check if a point $(x, y)$ lies on the line, substitute the $x$ and $y$ values into the equation and see if the equality holds. 3. **Substitute the point into the equation:** $$y = -2, \quad x = -2$$ $$-2 \stackrel{?}{=} -\frac{1}{3}(-2) + 9$$ 4. **Simplify the right side:** $$-\frac{1}{3}(-2) = \frac{2}{3}$$ So, $$-2 \stackrel{?}{=} \frac{2}{3} + 9$$ 5. **Add the terms on the right:** $$\frac{2}{3} + 9 = \frac{2}{3} + \frac{27}{3} = \frac{29}{3}$$ 6. **Compare both sides:** $$-2 = -\frac{6}{3} \neq \frac{29}{3}$$ 7. **Conclusion:** Since $$-2 \neq \frac{29}{3}$$, the point $(-2, -2)$ does not lie on the line $$y = -\frac{1}{3}x + 9$$.