Which of the following points is a solution to the linear inequality y>1/9x−2/9 ?(1 point)

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-coordinate of each point into the inequality and see if the y-coordinate satisfies it.

The inequality is \( y > \frac{1}{9}x - \frac{2}{9} \). Since all the given points have \( x = 0 \), we can simplify our calculations:

1. For \( (0, -\frac{4}{9}) \):
\[
y > \frac{1}{9}(0) - \frac{2}{9} \Rightarrow y > -\frac{2}{9}
\]
\(-\frac{4}{9} > -\frac{2}{9}\) is false.

2. For \( (0, -\frac{2}{9}) \):
\[
y > \frac{1}{9}(0) - \frac{2}{9} \Rightarrow y > -\frac{2}{9}
\]
\(-\frac{2}{9} > -\frac{2}{9}\) is false.

3. For \( (0, -\frac{1}{3}) \):
\[
y > \frac{1}{9}(0) - \frac{2}{9} \Rightarrow y > -\frac{2}{9}
\]
\(-\frac{1}{3} > -\frac{2}{9}\):
\(-\frac{1}{3} \approx -\frac{3}{9}\), so this is also false.

4. For \( (0, -\frac{1}{9}) \):
\[
y > \frac{1}{9}(0) - \frac{2}{9} \Rightarrow y > -\frac{2}{9}
\]
\(-\frac{1}{9} > -\frac{2}{9}\) is true.

Thus, the point that is a solution to the inequality \( y > \frac{1}{9}x - \frac{2}{9} \) is **(0, -\frac{1}{9})**.