To determine which of the given options is an ordered pair of the relation defined by the equation \( y = -23x + 6 \), we can substitute the \( x \)-values from each option into the equation and check if the corresponding \( y \)-value matches.
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For \( (0, -23) \): \[ y = -23(0) + 6 = 6 \quad \text{(not } -23\text{)} \]
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For \( \left(0, -\frac{2}{3}\right) \): \[ y = -23(0) + 6 = 6 \quad \text{(not } -\frac{2}{3}\text{)} \]
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For \( (1, 4) \): \[ y = -23(1) + 6 = -23 + 6 = -17 \quad \text{(not } 4\text{)} \]
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For \( (3, 4) \): \[ y = -23(3) + 6 = -69 + 6 = -63 \quad \text{(not } 4\text{)} \]
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For \( (3, 8) \): \[ y = -23(3) + 6 = -69 + 6 = -63 \quad \text{(not } 8\text{)} \]
None of the ordered pairs listed satisfies the equation \( y = -23x + 6 \). Each substitution yields a different result for \( y \) than that provided in the ordered pairs.
Thus, none of the given options is an ordered pair of the relation \( y = -23x + 6 \).