To determine which of the given points is a solution to the linear inequality \( y > 19x - 29 \), we can substitute the x-coordinates of each point into the inequality and check if the y-coordinates satisfy the inequality.
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For point \( (0, -13) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -13 > -29 \) (True).
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For point \( (0, -\frac{1}{3}) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -\frac{1}{3} > -29 \) (True).
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For point \( (0, -49) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -49 > -29 \) (False).
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For point \( (0, -\frac{4}{9}) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -\frac{4}{9} > -29 \) (True).
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For point \( (0, -19) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -19 > -29 \) (True).
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For point \( (0, -29) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -29 > -29 \) (False, since it needs to be greater than).
From the calculations, the points that satisfy the inequality \( y > 19x - 29 \) are:
- \( (0, -13) \)
- \( (0, -\frac{1}{3}) \)
- \( (0, -\frac{4}{9}) \)
- \( (0, -19) \)
Thus, any of the first four points are valid solutions, but the point \( (0, -29) \) is not.