To determine which of the provided ordered pairs is part of the relation \( y = -23x + 6 \), we can substitute the x-values from each ordered pair into the equation and see if the resulting y-value matches the y-value in the ordered pair.
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For the ordered pair \( (1, 4) \): \[ y = -23(1) + 6 = -23 + 6 = -17 \quad (\text{not } 4) \]
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For the ordered pair \( (3, 8) \): \[ y = -23(3) + 6 = -69 + 6 = -63 \quad (\text{not } 8) \]
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For the ordered pair \( (0, -23) \): \[ y = -23(0) + 6 = 0 + 6 = 6 \quad (\text{not } -23) \]
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For the ordered pair \( (3, 4) \): \[ y = -23(3) + 6 = -69 + 6 = -63 \quad (\text{not } 4) \]
None of the ordered pairs provided satisfy the relation \( y = -23x + 6 \).
So to summarize:
- \( (1, 4) \): y is not 4 (y = -17).
- \( (3, 8) \): y is not 8 (y = -63).
- \( (0, -23) \): y is not -23 (y = 6).
- \( (3, 4) \): y is not 4 (y = -63).
Thus, none of the options listed are ordered pairs of the relation.