To determine which of the given points is a solution to the linear inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we can substitute the x-value of each point into the inequality and check if the corresponding y-value satisfies it.
The inequality \( y > \frac{1}{9}x - \frac{2}{9} \) can be simplified for \( x = 0 \):
\[ y > \frac{1}{9}(0) - \frac{2}{9} \] \[ y > -\frac{2}{9} \]
Now we can check each point:
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Point (0, -1/9): \[ -\frac{1}{9} > -\frac{2}{9} \quad \text{(True)} \]
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Point (0, -4/9): \[ -\frac{4}{9} > -\frac{2}{9} \quad \text{(False)} \]
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Point (0, -2/9): \[ -\frac{2}{9} > -\frac{2}{9} \quad \text{(False)} \]
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Point (0, -1/3): \[ -\frac{1}{3} > -\frac{2}{9} \quad \text{(True since -1/3 is -3/9 and -3/9 > -2/9)} \]
The only points that satisfy the inequality are (0, -1/9) and (0, -1/3).
Therefore, the solution to the inequality is (0, -1/9).