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Select the correct set of ordered pairs for the given function and domain values:

Function:
[tex]\[ y = \frac{5}{3} x + 2 \][/tex]

Domain:
[tex]\[ \{-12, -3, 0, 3, 12\} \][/tex]

A. [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]

B. [tex]\(\{ (-12, -18), (-3, -3), (0, 2), (3, 7), (12, 22) \} \)[/tex]

C. [tex]\(\{ (-18, -12), (-3, -3), (2, 0), (7, 3), (22, 12) \} \)[/tex]

D. [tex]\(\left\{ (-12, -\frac{42}{5}), (-3, -3), (0, -\frac{6}{5}), (3, \frac{3}{5}), (12, 6) \right\} \)[/tex]



Answer :

GinnyAnswer
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.

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