Which of the following is an ordered pair of the relation y=−2/3x+6 ?(1 point) Responses (1,4) left parenthesis 1 comma 4 right parenthesis (3,4) left parenthesis 3 comma 4 right parenthesis (3,8) left parenthesis 3 comma 8 right parenthesis (0,−2/3)
To determine which of the given pairs is an ordered pair of the relation \( y = -\frac{2}{3}x + 6 \), we can plug the x-values of the pairs into the equation and check if the y-values match the result.
Let's examine each pair:
1. \( (1, 4) \)
For \( x = 1 \):
\[ y = -\frac{2}{3}(1) + 6 = -\frac{2}{3} + 6 = \frac{18}{3} - \frac{2}{3} = \frac{16}{3} \]
Since \( \frac{16}{3} \neq 4 \), this pair does not satisfy the equation.
2. \( (3, 4) \)
For \( x = 3 \):
\[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \]
This matches the given y-value, so \( (3, 4) \) is an ordered pair of the relation.
3. \( (3, 8) \)
For \( x = 3 \):
\[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \]
Since \( 4 \neq 8 \), this pair does not satisfy the equation.
4. \( (0, -\frac{2}{3}) \)
For \( x = 0 \):
\[ y = -\frac{2}{3}(0) + 6 = 0 + 6 = 6 \]
Since \( 6 \neq -\frac{2}{3} \), this pair does not satisfy the equation.
The only ordered pair from the given options that is part of the relation \( y = -\frac{2}{3}x + 6 \) is \( (3, 4) \).