To determine which point is a solution to the inequality \( y > 19x - 29 \), we will substitute the x-coordinate of each point into the inequality and check if the y-coordinate satisfies it.
The inequality is:
\[ y > 19x - 29 \]
Now, let’s evaluate each point:
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Point (0, -49): \[ y = -49, \quad x = 0 \] \[ -49 > 19(0) - 29 \quad \Rightarrow \quad -49 > -29 \quad \text{(False)} \]
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Point \(\left(0, -\frac{4}{9}\right)\): \[ y = -\frac{4}{9}, \quad x = 0 \] \[ -\frac{4}{9} > 19(0) - 29 \quad \Rightarrow \quad -\frac{4}{9} > -29 \quad \text{(True)} \]
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Point (0, -29): \[ y = -29, \quad x = 0 \] \[ -29 > 19(0) - 29 \quad \Rightarrow \quad -29 > -29 \quad \text{(False)} \]
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Point \(\left(0, -\frac{2}{9}\right)\): \[ y = -\frac{2}{9}, \quad x = 0 \] \[ -\frac{2}{9} > 19(0) - 29 \quad \Rightarrow \quad -\frac{2}{9} > -29 \quad \text{(True)} \]
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Point (0, -19): \[ y = -19, \quad x = 0 \] \[ -19 > 19(0) - 29 \quad \Rightarrow \quad -19 > -29 \quad \text{(True)} \]
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Point (0, -13): \[ y = -13, \quad x = 0 \] \[ -13 > 19(0) - 29 \quad \Rightarrow \quad -13 > -29 \quad \text{(True)} \]
From the evaluations:
- \(\left(0, -\frac{4}{9}\right)\): True
- \(\left(0, -\frac{2}{9}\right)\): True
- (0, -19): True
- (0, -13): True
The only point that satisfies the inequality is \(\left(0, -\frac{4}{9}\right)\).
Thus, the point, which is a solution to the inequality \( y > 19x - 29 \), is:
\(\left(0, -\frac{4}{9}\right)\).