To determine which of the options is an ordered pair in the relation represented by the equation \( y = -\frac{2}{3}x + 6 \), we can substitute the \( x \)-values from the ordered pairs into the equation and see if we get the corresponding \( y \)-value.
Let's check each option:
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For (1, 4): \[ y = -\frac{2}{3}(1) + 6 = -\frac{2}{3} + 6 = \frac{16}{3} \quad \text{(This is not 4)} \]
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For (-3, 3): \[ y = -\frac{2}{3}(-3) + 6 = 2 + 6 = 8 \quad \text{(This is not 3)} \]
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For (3, 8): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \quad \text{(This is not 8)} \]
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For (3, 4): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \quad \text{(This is correct)} \]
The correct ordered pair is (3, 4).