Use the table to answer the question.

Raspberry Lemonade
1 2.5
2 5
4 10
6 15
Rosie is planning to make raspberry lemonade for a party. She needs to add 2 scoops of raspberry to every 5 cups of lemonade. The data table shows the ratios needed. At what ratio does the constant of proportionality appear?

(1 point)
Responses

(1, 2.5)
left parenthesis 1 comma 2.5 right parenthesis

(2, 5)
left parenthesis 2 comma 5 right parenthesis

(5, 2)
left parenthesis 5 comma 2 right parenthesis

(2.5, 1)

1 answer

To find the constant of proportionality from the given data table, we need to look at the relationship between the two quantities: the amount of raspberry and the amount of lemonade.

The constant of proportionality is the ratio of raspberry to lemonade. We'll find the ratio for each pair in the table:

  • For (1, 2.5), the ratio is \( \frac{1}{2.5} = 0.4 \)
  • For (2, 5), the ratio is \( \frac{2}{5} = 0.4 \)
  • For (4, 10), the ratio is \( \frac{4}{10} = 0.4 \)
  • For (6, 15), the ratio is \( \frac{6}{15} = 0.4 \)

All ratios equal 0.4, which indicates a constant relationship between raspberry and lemonade.

Given the options:

  • (1, 2.5)
  • (2, 5)
  • (5, 2)
  • (2.5, 1)

The correct answers reflecting the constant ratio of raspberry to lemonade are (1, 2.5) and (2, 5). However, since the question asks for the ratio in which the constant of proportionality appears, the most straightforward ratios showing how much raspberry is needed relative to lemonade is in response to Rosie needing 2 scoops of raspberry for every 5 cups of lemonade.

Accordingly, the best answer that clearly illustrates the constant of proportionality would be (2, 5), as it shows 2 scoops of raspberry to 5 cups of lemonade directly.

So the final answer is (2, 5).