Question

Which is an ordered pair of the relation y=2/3x−5
?

Show your work.

(1 point)
Responses

(9, 2)
(9, 2)

(−3, 7)
(−3, 7)

(6,−1)
open paren 6 comma negative 1 close paren

(3, 3)

Answer 1

To determine which of the given pairs is an ordered pair of the relation \( y = \frac{2}{3}x - 5 \), we will substitute the \( x \) value from each ordered pair into the equation and check if the corresponding \( y \) value from the pair is equal to the result.

1. **For the pair (9, 2)**:
\[
y = \frac{2}{3}(9) - 5 = 6 - 5 = 1
\]
Since \( 2 \neq 1 \), this pair is not on the line.

2. **For the pair (-3, 7)**:
\[
y = \frac{2}{3}(-3) - 5 = -2 - 5 = -7
\]
Since \( 7 \neq -7 \), this pair is not on the line.

3. **For the pair (6, -1)**:
\[
y = \frac{2}{3}(6) - 5 = 4 - 5 = -1
\]
Since \( -1 = -1 \), this pair is on the line.

4. **For the pair (3, 3)**:
\[
y = \frac{2}{3}(3) - 5 = 2 - 5 = -3
\]
Since \( 3 \neq -3 \), this pair is not on the line.

The only ordered pair that satisfies the equation \( y = \frac{2}{3}x - 5 \) is **(6, -1)**.