To determine the correct set of ordered pairs, we first apply the given function [tex]\( y = \frac{5}{3}x + 2 \)[/tex] to each of the domain values [tex]\( \{-12, -3, 0, 3, 12\} \)[/tex].
1. For [tex]\( x = -12 \)[/tex]:
[tex]\( y = \frac{5}{3}(-12) + 2 \)[/tex]
[tex]\( y = -20 + 2 \)[/tex]
[tex]\( y = -18 \)[/tex]
So, the ordered pair is [tex]\((-12, -18)\)[/tex].
2. For [tex]\( x = -3 \)[/tex]:
[tex]\( y = \frac{5}{3}(-3) + 2 \)[/tex]
[tex]\( y = -5 + 2 \)[/tex]
[tex]\( y = -3 \)[/tex]
So, the ordered pair is [tex]\((-3, -3)\)[/tex].
3. For [tex]\( x = 0 \)[/tex]:
[tex]\( y = \frac{5}{3}(0) + 2 \)[/tex]
[tex]\( y = 0 + 2 \)[/tex]
[tex]\( y = 2 \)[/tex]
So, the ordered pair is [tex]\((0, 2)\)[/tex].
4. For [tex]\( x = 3 \)[/tex]:
[tex]\( y = \frac{5}{3}(3) + 2 \)[/tex]
[tex]\( y = 5 + 2 \)[/tex]
[tex]\( y = 7 \)[/tex]
So, the ordered pair is [tex]\((3, 7)\)[/tex].
5. For [tex]\( x = 12 \)[/tex]:
[tex]\( y = \frac{5}{3}(12) + 2 \)[/tex]
[tex]\( y = 20 + 2 \)[/tex]
[tex]\( y = 22 \)[/tex]
So, the ordered pair is [tex]\((12, 22)\)[/tex].
Hence, the correct set of ordered pairs is:
[tex]\[ \{(-12, -18), (-3, -3), (0, 2), (3, 7), (12, 22)\} \][/tex]
Therefore, the correct answer is B.
