Question

which of the following is an ordered pair of the relation y=−2/3x+6 A. (0, 2/3) B. (3,8). C. (3,4). D.(1,4)

Answer 1

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.

1. **Option A: (0, \( \frac{2}{3} \))**

\( x = 0 \):
\( y = -\frac{2}{3}(0) + 6 = 6 \)
The ordered pair is (0, 6), not (0, \( \frac{2}{3} \)).

2. **Option B: (3, 8)**

\( x = 3 \):
\( y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \)
The ordered pair is (3, 4), not (3, 8).

3. **Option C: (3, 4)**

\( x = 3 \):
\( y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \)
The ordered pair is (3, 4), which matches.

4. **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)**.