Which of the following is an ordered pair of the relation y = - 2/3x + 6? (1 point)
O (3,4)
0 (0, -2/3)
• (3,8)
• (1, 4)
To find out which of the following is an ordered pair of the relation \( y = -\frac{2}{3}x + 6 \), you can simply plug the x-values of each ordered pair into the equation and see if the corresponding y-value matches.
Let's test each option:
1) (3,4)
Plugging in \( x = 3 \) into the relation, we get:
\( y = -\frac{2}{3} \times 3 + 6 \)
\( y = -2 + 6 \)
\( y = 4 \)
Since \( y = 4 \) is the same as the y-value in the ordered pair (3,4), this ordered pair is a part of the relation.
2) (0, -2/3)
Plugging in \( x = 0 \) into the relation, we get:
\( y = -\frac{2}{3} \times 0 + 6 \)
\( y = 0 + 6 \)
\( y = 6 \)
Since \( y = 6 \) is not the same as the y-value in the ordered pair (0, -2/3), this ordered pair is not a part of the relation.
3) (3,8)
Plugging in \( x = 3 \) into the relation again:
\( y = -\frac{2}{3} \times 3 + 6 \)
\( y = -2 + 6 \)
\( y = 4 \)
Since \( y = 4 \) and not 8, the ordered pair (3,8) is not a part of the relation.
4) (1, 4)
Plugging in \( x = 1 \) into the relation, we get:
\( y = -\frac{2}{3} \times 1 + 6 \)
\( y = -\frac{2}{3} + 6 \)
We need to convert 6 into thirds to add it to -2/3:
\( 6 = \frac{18}{3} \)
Now we can add them:
\( y = -\frac{2}{3} + \frac{18}{3} \)
\( y = \frac{16}{3} \)
The value \( \frac{16}{3} \) does not simplify to 4, so the ordered pair (1,4) is not a part of the relation.
Finally, the first option (3,4) is the only correct ordered pair of the relation \( y = -\frac{2}{3}x + 6 \).