To determine which of the points is a solution to the linear inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we can substitute the x-coordinates of each point into the inequality and see if the corresponding y-coordinates satisfy it.
The inequality can be expressed for \( x = 0 \):
\[ y > \frac{1}{9}(0) - \frac{2}{9} \] \[ y > -\frac{2}{9} \]
Now we can check each point:
A: \( (0, -\frac{2}{9}) \)
- Substitute \( y = -\frac{2}{9} \): \[ -\frac{2}{9} > -\frac{2}{9} \quad \text{(false)} \]
B: \( (0, -\frac{4}{9}) \)
- Substitute \( y = -\frac{4}{9} \): \[ -\frac{4}{9} > -\frac{2}{9} \quad \text{(false)} \]
C: \( (0, -\frac{1}{3}) \)
- Substitute \( y = -\frac{1}{3} \approx -\frac{3}{9} \): \[ -\frac{1}{3} > -\frac{2}{9} \quad \text{(false)} \]
D: \( (0, -\frac{1}{9}) \)
- Substitute \( y = -\frac{1}{9} \): \[ -\frac{1}{9} > -\frac{2}{9} \quad \text{(true)} \]
The only point that satisfies the inequality is:
D: \( (0, -\frac{1}{9}) \).