To determine which of the given pairs is an ordered pair of the relation \( y = -\frac{2}{3}x + 6 \), we can substitute the \( x \) value from each ordered pair into the equation and check if it results in the corresponding \( y \) value.
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For the pair \( (1, 4) \): \[ y = -\frac{2}{3}(1) + 6 = -\frac{2}{3} + 6 = -\frac{2}{3} + \frac{18}{3} = \frac{16}{3} \quad (\text{not } 4) \]
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For the pair \( (0, -\frac{2}{3}) \): \[ y = -\frac{2}{3}(0) + 6 = 0 + 6 = 6 \quad (\text{not } -\frac{2}{3}) \]
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For the pair \( (3, 8) \): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \quad (\text{not } 8) \]
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For the pair \( (3, 4) \): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \quad (\text{this is correct}) \]
The only ordered pair that corresponds to the relation \( y = -\frac{2}{3}x + 6 \) is \( (3, 4) \).