To determine which ordered pair [tex]\((x, y)\)[/tex] could be the missing values in the table, we can use the function [tex]\(y = 16 + 0.5x\)[/tex]. Following is a step-by-step solution:
1. Identify the given values:
For each [tex]\(x\)[/tex], the corresponding [tex]\(y\)[/tex] is calculated using:
[tex]\[
y = 16 + 0.5x
\][/tex]
2. Compute [tex]\(y\)[/tex] for each provided [tex]\(x\)[/tex] in the ordered pairs:
- For [tex]\( (x, y) = (0, 18) \)[/tex]:
[tex]\[
y = 16 + 0.5(0) = 16 \quad \rightarrow \; y \, \textbf{is not}\, 18
\][/tex]
- For [tex]\( (x, y) = (5, 19.5) \)[/tex]:
[tex]\[
y = 16 + 0.5(5) = 16 + 2.5 = 18.5 \quad \rightarrow \; y \, \textbf{is not}\, 19.5
\][/tex]
- For [tex]\( (x, y) = (8, 20) \)[/tex]:
[tex]\[
y = 16 + 0.5(8) = 16 + 4 = 20 \quad \rightarrow \; y \, \textbf{could be}\, 20
\][/tex]
- For [tex]\( (x, y) = (10, 21.5) \)[/tex]:
[tex]\[
y = 16 + 0.5(10) = 16 + 5 = 21 \quad \rightarrow \; y \, \textbf{is not}\, 21.5
\][/tex]
3. Compare Calculations with Provided Ordered Pairs:
The calculated [tex]\( y \)[/tex] values verify if the pairs are accurate or not with the function:
- [tex]\((0, 18)\)[/tex] does not match
- [tex]\((5, 19.5)\)[/tex] does not match
- [tex]\((8, 20)\)[/tex] matches
- [tex]\((10, 21.5)\)[/tex] does not match
4. Conclusion:
Therefore, the ordered pair [tex]\((8, 20)\)[/tex] [tex]\( \)[/tex] meets the conditions of the function [tex]\( y = 16 + 0.5x \)[/tex] fitting [tex]\( y = 20 \)[/tex] exactly. Hence, the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] pair that can be represented by the missing values is:
[tex]\[
\boxed{(8, 20)}
\][/tex]
