To determine the correct set of ordered pairs, we need to evaluate the given function [tex]\( y = \frac{5}{3} x + 2 \)[/tex] over the specified domain values [tex]\( \{-12, -3, 0, 3, 12\} \)[/tex].
Let's compute each value step by step.
1. For [tex]\( x = -12 \)[/tex]:
[tex]\[
y = \frac{5}{3}(-12) + 2 = -20 + 2 = -18
\][/tex]
Thus, the ordered pair is [tex]\((-12, -18)\)[/tex].
2. For [tex]\( x = -3 \)[/tex]:
[tex]\[
y = \frac{5}{3}(-3) + 2 = -5 + 2 = -3
\][/tex]
Thus, the ordered pair is [tex]\((-3, -3)\)[/tex].
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = \frac{5}{3}(0) + 2 = 0 + 2 = 2
\][/tex]
Thus, the ordered pair is [tex]\((0, 2)\)[/tex].
4. For [tex]\( x = 3 \)[/tex]:
[tex]\[
y = \frac{5}{3}(3) + 2 = 5 + 2 = 7
\][/tex]
Thus, the ordered pair is [tex]\((3, 7)\)[/tex].
5. For [tex]\( x = 12 \)[/tex]:
[tex]\[
y = \frac{5}{3}(12) + 2 = 20 + 2 = 22
\][/tex]
Thus, the ordered pair is [tex]\((12, 22)\)[/tex].
Now, let's compare our ordered pairs [tex]\( \{(-12, -18), (-3, -3), (0, 2), (3, 7), (12, 22)\} \)[/tex] with the options provided:
- Option A: [tex]\(\{(-18, -12), (-3, -3), (2, 0), (7, 3), (22, 12)\}\)[/tex]
- Option B: [tex]\(\left\{\left(-\frac{42}{5}, -12\right), (-3, -3), \left(-\frac{6}{5}, 0\right), \left(\frac{3}{5}, 3\right), (6, 12)\right\}\)[/tex]
- Option C: [tex]\(\left\{\left(-12, -\frac{42}{5}\right), (-3, -3), \left(0, -\frac{6}{5}\right), \left(3, \frac{3}{5}\right), (12, 6)\right\}\)[/tex]
- Option D: [tex]\(\{(-12, -18), (-3, -3), (0, 2), (3, 7), (12, 22)\}\)[/tex]
The correct option is Option D.
