To determine which of the given points is a solution to the linear inequality \( y > 19x - 29 \), we can substitute the x-coordinate of each point into the inequality and see if the corresponding value of y satisfies the inequality.
For each point, the x-coordinate is \( 0 \). So, we substitute \( x = 0 \) into the inequality:
\[ y > 19(0) - 29 \] \[ y > -29 \]
Now we will evaluate each of the given points:
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Point (0, -49): \[ -49 > -29 \quad \text{(False)} \]
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Point \( \left(0, -\frac{4}{9}\right) \): \[ -\frac{4}{9} > -29 \quad \text{(True)} \]
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Point (0, -19): \[ -19 > -29 \quad \text{(True)} \]
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Point \( \left(0, -\frac{1}{9}\right) \): \[ -\frac{1}{9} > -29 \quad \text{(True)} \]
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Point (0, -29): \[ -29 > -29 \quad \text{(False)} \]
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Point \( (0, -13) \): \[ -13 > -29 \quad \text{(True)} \]
The points that satisfy the inequality \( y > -29 \) are:
- \( \left(0, -\frac{4}{9}\right) \)
- (0, -19)
- \( \left(0, -\frac{1}{9}\right) \)
- (0, -13)
Among these, any of them can be considered a valid solution to the inequality \( y > 19x - 29 \).
If you are looking for one specific point as an answer, one of the options would be \( \left(0, -\frac{4}{9}\right) \).