To determine if the price of chicken wings at Buffalo Mild Wings is proportional to the number of wings you order, we need to analyze the given data.
We have:
- Number of wings ordered ([tex]\(x\)[/tex]): 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
- Corresponding prices ([tex]\(y\)[/tex]): 10, 8, 6, 2
Proportional means that the ratio of price per wing should remain constant across different orders.
Step-by-Step Solution:
1. Identify Pairs:
We have a collection of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values, which form pairs [tex]\((x, y)\)[/tex].
2. Calculate Ratios:
For proportionality, the ratios of [tex]\(\frac{y}{x}\)[/tex] for each pair should be constant. We need to determine the ratios for each combination of [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Note: For simplicity, not every combination needs checking, as consistent proportionality implies all ratios will match.
Let's compute a few ratio examples explicitly:
- [tex]\(\frac{10}{2} = 5\)[/tex]
- [tex]\(\frac{10}{4} = 2.5\)[/tex]
- [tex]\(\frac{8}{2} = 4\)[/tex]
- [tex]\(\frac{8}{4} = 2\)[/tex]
3. Compare Ratios:
- Examining the few calculated values, we see:
[tex]\(\frac{10}{2} \neq \frac{8}{2}\)[/tex] (5 [tex]\(\neq\)[/tex] 4)
[tex]\(\frac{10}{4} \neq \frac{8}{4}\)[/tex] (2.5 [tex]\(\neq\)[/tex] 2)
4. Conclusion:
Since the ratios [tex]\(\frac{y}{x}\)[/tex] are not constant across the different combinations of [tex]\(x\)[/tex] and [tex]\(y\)[/tex], the price of chicken wings is not proportional to the number of wings ordered.
Based on the analysis, the correct answer is:
- B: No
