To determine which point is a solution to the linear inequality \( y > 19x - 29 \), we will evaluate each point by substituting the \( x \) and \( y \) coordinates into the inequality.
The inequality is: \[ y > 19x - 29 \]
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For the point (0, -29): \[ y = -29, \quad x = 0 \] \[ -29 > 19(0) - 29 \] \[ -29 > -29 \quad \text{(false)} \]
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For the point (0, -2/9): \[ y = -\frac{2}{9}, \quad x = 0 \] \[ -\frac{2}{9} > 19(0) - 29 \] \[ -\frac{2}{9} > -29 \quad \text{(true)} \]
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For the point (0, -19): \[ y = -19, \quad x = 0 \] \[ -19 > 19(0) - 29 \] \[ -19 > -29 \quad \text{(true)} \]
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For the point (0, -13): \[ y = -13, \quad x = 0 \] \[ -13 > 19(0) - 29 \] \[ -13 > -29 \quad \text{(true)} \]
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For the point (0, -49): \[ y = -49, \quad x = 0 \] \[ -49 > 19(0) - 29 \] \[ -49 > -29 \quad \text{(false)} \]
Thus, the points that are solutions to the inequality \( y > 19x - 29 \) are:
- \( (0, -\frac{2}{9}) \)
- \( (0, -19) \)
- \( (0, -13) \)
Therefore, any of the points \( (0, -\frac{2}{9}) \), \( (0, -19) \), or \( (0, -13) \) can be considered a solution to the inequality.