To determine which of the given options is an ordered pair of the relation \( y = -\frac{2}{3}x + 6 \), we can substitute the x-coordinate of each option into the equation and see if we get the corresponding y-coordinate.
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Option A: (0, \( \frac{2}{3} \))
\( x = 0 \):
\( y = -\frac{2}{3}(0) + 6 = 6 \)
The ordered pair is (0, 6), not (0, \( \frac{2}{3} \)). -
Option B: (3, 8)
\( x = 3 \):
\( y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \)
The ordered pair is (3, 4), not (3, 8). -
Option C: (3, 4)
\( x = 3 \):
\( y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \)
The ordered pair is (3, 4), which matches. -
Option D: (1, 4)
\( x = 1 \):
\( y = -\frac{2}{3}(1) + 6 = -\frac{2}{3} + 6 \)
Converting 6 to thirds: \( 6 = \frac{18}{3} \)
Therefore, \( y = \frac{18}{3} - \frac{2}{3} = \frac{16}{3} \)
This does not match (1, 4).
The only correct ordered pair for the relation \( y = -\frac{2}{3}x + 6 \) is C. (3, 4).