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 (which are all 0) into the inequality and see if the corresponding y-coordinates satisfy it.
The inequality simplifies to: \[ y > 19(0) - 29 \] \[ y > -29 \]
Now, we will check each point to see if its y-coordinate is greater than -29.
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Point (0, -49): \[ -49 > -29 \] → False
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Point \( \left(0, -\frac{4}{9}\right) \): \[ -\frac{4}{9} > -29 \] → True (since -4/9 is greater than -29)
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Point (0, -19): \[ -19 > -29 \] → True
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Point \( \left(0, -\frac{1}{9}\right) \): \[ -\frac{1}{9} > -29 \] → True
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Point (0, -29): \[ -29 > -29 \] → False
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Point \( \left(0, -\frac{2}{9}\right) \): \[ -\frac{2}{9} > -29 \] → True
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Point (0, -13): \[ -13 > -29 \] → True
From the checks above, the following points satisfy the inequality \( y > -29 \):
- \( \left(0, -\frac{4}{9}\right) \)
- (0, -19)
- \( \left(0, -\frac{1}{9}\right) \)
- \( \left(0, -\frac{2}{9}\right) \)
- (0, -13)
Thus, the points (0, -19), \( \left(0, -\frac{4}{9}\right) \), \( \left(0, -\frac{1}{9}\right) \), \( \left(0, -\frac{2}{9}\right) \), and (0, -13) are solutions to the inequality.
Depending on the specific wording of the question, the response could refer to any of these valid points. If you need one specific point, I suggest \( (0, -19) \) as it is one of the responses listed in the original options.