To determine which of the given ordered pairs is a solution to the relation \( y = -\frac{2}{3}x + 6 \), we can substitute the x-value of each ordered pair into the equation and see if the resultant y-value matches the one in the pair.
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For the ordered pair \( (3, 4) \): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \] So, \( (3, 4) \) is a solution.
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For the ordered pair \( (3, 8) \): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \] This does not match \( y = 8 \).
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For the ordered pair \( (0, -\frac{2}{3}) \): \[ y = -\frac{2}{3}(0) + 6 = 0 + 6 = 6 \] This does not match \( y = -\frac{2}{3} \).
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For the ordered pair \( (1, 4) \): \[ y = -\frac{2}{3}(1) + 6 = -\frac{2}{3} + 6 = 5 + \frac{4}{3} = \frac{18}{3} + \frac{4}{3} = \frac{22}{3} \approx 7.33 \] This does not match \( y = 4 \).
The only ordered pair that is a solution to the equation \( y = -\frac{2}{3}x + 6 \) is \( (3, 4) \).
Thus, the correct response is: (3, 4).