To determine which of the given points is a solution to the inequality \( y > 19x - 29 \), we can substitute the \( x \) and \( y \) values from each point into the inequality and check if it holds true.
The inequality in terms of \( x \) and \( y \) is:
\[ y > 19x - 29 \]
Let's evaluate each option by substituting \( x = 0 \) into the inequality.
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Point (0, -13): \[ -13 > 19(0) - 29 \implies -13 > -29 \quad \text{(True)} \]
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Point \( \left(0, -\frac{1}{3}\right) \): \[ -\frac{1}{3} > 19(0) - 29 \implies -\frac{1}{3} > -29 \quad \text{(True)} \]
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Point (0, -19): \[ -19 > 19(0) - 29 \implies -19 > -29 \quad \text{(True)} \]
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Point \( \left(0, -\frac{4}{9}\right) \): \[ -\frac{4}{9} > 19(0) - 29 \implies -\frac{4}{9} > -29 \quad \text{(True)} \]
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Point (0, -29): \[ -29 > 19(0) - 29 \implies -29 > -29 \quad \text{(False)} \]
Based on the evaluations, all points except (0, -29) satisfy the inequality \( y > 19x - 29 \). Therefore, the solutions to the inequality are:
- (0, -13)
- \( \left(0, -\frac{1}{3}\right) \)
- (0, -19)
- \( \left(0, -\frac{4}{9}\right) \)
Hence, any of the first four points can be considered a solution, but the first four options listed are valid responses.
3 answers