To determine which of the given points is a solution to the inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we will substitute the x-coordinates of the points into the inequality.
Since all the provided points have an x-coordinate of 0, we can substitute \( x = 0 \) into the inequality:
\[ y > \frac{1}{9}(0) - \frac{2}{9} \] \[ y > -\frac{2}{9} \]
Now we can evaluate each point:
A. \( (0, -\frac{2}{9}) \)
Substituting \( y = -\frac{2}{9} \):
\[
-\frac{2}{9} > -\frac{2}{9} \quad \text{(false)}
\]
B. \( (0, -\frac{4}{9}) \)
Substituting \( y = -\frac{4}{9} \):
\[
-\frac{4}{9} > -\frac{2}{9} \quad \text{(false)}
\]
C. \( (0, -\frac{1}{3}) \)
Substituting \( y = -\frac{1}{3} \) (which is equal to \(-\frac{3}{9}\)):
\[
-\frac{3}{9} > -\frac{2}{9} \quad \text{(false)}
\]
D. \( (0, -\frac{1}{9}) \)
Substituting \( y = -\frac{1}{9} \):
\[
-\frac{1}{9} > -\frac{2}{9} \quad \text{(true)}
\]
Only point D is greater than \(-\frac{2}{9}\).
So, the solution to the linear inequality is: D. (0, -1/9)