To determine which of the given points is a solution to the inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we can substitute the x-coordinate of each point into the equation and check if the resulting y-value is greater than the corresponding value calculated from the inequality.
The inequality can be rewritten as: \[ y > \frac{1}{9}x - \frac{2}{9} \]
Since all the points have \( x = 0 \), we substitute \( x = 0 \) into the inequality:
\[ y > \frac{1}{9}(0) - \frac{2}{9} \] \[ y > -\frac{2}{9} \]
Now we check each point:
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(0, -19): \(-19 > -\frac{2}{9}\) → False (Not a solution)
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(0, -2/9): \(-\frac{2}{9} > -\frac{2}{9}\) → False (Not a solution; note it should be greater, not equal)
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(0, -1/3): \(-\frac{1}{3} > -\frac{2}{9}\) →
- Convert to a common denominator (9): \(-\frac{1}{3} = -\frac{3}{9}\)
- Therefore, \(-\frac{3}{9} > -\frac{2}{9}\) → False (Not a solution)
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(0, -4/9): \(-\frac{4}{9} > -\frac{2}{9}\) → False (Not a solution)
None of the given points satisfy the inequality \( y > \frac{1}{9}x - \frac{2}{9} \).
Please double-check the inequality or the points provided.