To determine which points are solutions 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 resulting y-coordinate is greater than the expression on the right-hand side.
The inequality is:
\[ y > \frac{1}{9}x - \frac{2}{9} \]
For x = 0, the inequality simplifies to:
\[ y > \frac{1}{9}(0) - \frac{2}{9} \implies y > -\frac{2}{9} \]
Now we check each given point:
-
Point (0, -49):
- y = -49
- Check: -49 > -2/9 (False)
-
Point \( (0, -\frac{4}{9}) \):
- y = -\( \frac{4}{9} \)
- Check: -\( \frac{4}{9} \) > -\( \frac{2}{9} \) (False)
-
Point (0, -29):
- y = -29
- Check: -29 > -2/9 (False)
-
Point \( (0, -\frac{2}{9}) \):
- y = -\( \frac{2}{9} \)
- Check: -\( \frac{2}{9} \) > -\( \frac{2}{9} \) (False)
-
Point (0, -13):
- y = -13
- Check: -13 > -2/9 (False)
-
Point \( (0, -\frac{1}{3}) \):
- y = -\( \frac{1}{3} \) (which is -\( \frac{3}{9} \))
- Check: -\( \frac{3}{9} \) > -\( \frac{2}{9} \) (False)
-
Point (0, -19):
- y = -19
- Check: -19 > -2/9 (False)
It appears that none of the given points satisfy the inequality \( y > -\frac{2}{9} \).
Please double-check the points or provide other options if the problem context allows prevailing confirmations.