To determine which of the given points is a solution to the linear inequality \( y > 19x - 29 \), we will substitute the x-coordinates of each point into the inequality and see if the resulting y-value satisfies the inequality.
The inequality is: \[ y > 19x - 29 \]
Now, we will evaluate each point:
-
Point (0, -29):
- Substitute \( x = 0 \): \[ y > 19(0) - 29 \implies y > -29 \]
- Check: \( -29 > -29 \) (false). This point does not satisfy the inequality.
-
Point \( (0, -\frac{2}{9}) \):
- Substitute \( x = 0 \): \[ y > 19(0) - 29 \implies y > -29 \]
- Check: \( -\frac{2}{9} > -29 \) (true). This point satisfies the inequality.
-
Point (0, -49):
- Substitute \( x = 0 \): \[ y > 19(0) - 29 \implies y > -29 \]
- Check: \( -49 > -29 \) (false). This point does not satisfy the inequality.
-
Point \( (0, -\frac{4}{9}) \):
- Substitute \( x = 0 \): \[ y > 19(0) - 29 \implies y > -29 \]
- Check: \( -\frac{4}{9} > -29 \) (true). This point also satisfies the inequality.
-
Point (0, -19):
- Substitute \( x = 0 \): \[ y > 19(0) - 29 \implies y > -29 \]
- Check: \( -19 > -29 \) (true). This point satisfies the inequality.
-
Point (0, -13):
- Substitute \( x = 0 \): \[ y > 19(0) - 29 \implies y > -29 \]
- Check: \( -13 > -29 \) (true). This point satisfies the inequality.
From the evaluations above, the following points satisfy the inequality \( y > 19x - 29 \):
- \( (0, -\frac{2}{9}) \)
- \( (0, -\frac{4}{9}) \)
- \( (0, -19) \)
- \( (0, -13) \)
However, since the question requests a single point, we can conclude that:
- The point \( (0, -\frac{2}{9}) \) is one valid solution.
So, the answer is \( (0, -\frac{2}{9}) \).