To determine which point is a solution to the inequality \( y > 19x - 29 \), we will substitute the \( x \) values of the points into the inequality and check if the resulting inequality holds true for the corresponding \( y \) values.
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For the point \( (0, -29) \): \[ y > 19(0) - 29 \implies -29 > -29 \quad \text{(False)} \]
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For the point \( (0, -\frac{2}{9}) \): \[ y > 19(0) - 29 \implies -\frac{2}{9} > -29 \quad \text{(True)} \]
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For the point \( (0, -49) \): \[ y > 19(0) - 29 \implies -49 > -29 \quad \text{(False)} \]
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For the point \( (0, -\frac{4}{9}) \): \[ y > 19(0) - 29 \implies -\frac{4}{9} > -29 \quad \text{(True)} \]
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For the point \( (0, -19) \): \[ y > 19(0) - 29 \implies -19 > -29 \quad \text{(True)} \]
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For the point \( (0, -\frac{1}{9}) \): \[ y > 19(0) - 29 \implies -\frac{1}{9} > -29 \quad \text{(True)} \]
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For the point \( (0, -13) \): \[ y > 19(0) - 29 \implies -13 > -29 \quad \text{(True)} \]
From this analysis, the following points are solutions to the inequality \( y > 19x - 29 \):
- \( (0, -\frac{2}{9}) \)
- \( (0, -\frac{4}{9}) \)
- \( (0, -19) \)
- \( (0, -\frac{1}{9}) \)
- \( (0, -13) \)
Out of the options given, the only point that clearly holds true as a direct response is:
- \( (0, -\frac{4}{9}) \) But also any of the other direct points also work correctly: \( (0, -19) \) or \( (0, -13) \).
The best conclusive response in this case comes down to the verification that the points (0, -2/9), (0, -19), (0, 0.11) show the correct data.
1 answer