Which of the following is an ordered pair of the relation y=−2/3x+6

Question

?(1 point)
Responses

(3,4)
left parenthesis 3 comma 4 right parenthesis

(3,8)
left parenthesis 3 comma 8 right parenthesis

(0,−2/3)
left parenthesis 0 comma negative Start Fraction 2 over 3 End Fraction right parenthesis

(1,4)

Answer 1

To determine which of the given ordered pairs is part of the relation defined by the equation \( y = -\frac{2}{3}x + 6 \), we can substitute the x-value of each ordered pair into the equation and see if the resulting y-value matches the second number in the pair.

1. For (3, 4):

   \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \]

   This pair is valid, as \( y = 4 \).

2. For (3, 8):

   \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \]

   This pair is not valid, as \( y \neq 8 \).

3. For (0, -\frac{2}{3}):

   \[ y = -\frac{2}{3}(0) + 6 = 0 + 6 = 6 \]

   This pair is not valid, as \( y \neq -\frac{2}{3} \).

4. For (1, 4):

   \[ y = -\frac{2}{3}(1) + 6 = -\frac{2}{3} + 6 = \frac{-2 + 18}{3} = \frac{16}{3} \]

   This pair is not valid, as \( y \neq 4 \).

The only ordered pair that satisfies the equation is (3, 4).