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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

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

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

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

(5, 2)

1 answer

To find the constant of proportionality from the table, we need to identify the ratio of raspberry to lemonade. The key represents the number of scoops of raspberry for a certain number of cups of lemonade.

Given the ratios in the table:

  • At (1, 2.5): 1 scoop of raspberry for 2.5 cups of lemonade
  • At (2, 5): 2 scoops of raspberry for 5 cups of lemonade
  • At (4, 10): 4 scoops of raspberry for 10 cups of lemonade
  • At (6, 15): 6 scoops of raspberry for 15 cups of lemonade

We can see that the ratios are consistent; it maintains the same relationship between raspberry and lemonade.

The ratio of raspberry to lemonade is constantly \( \frac{1}{2.5} \) or \( \frac{2}{5} \).

Thus, the constant of proportionality appears at the ratio \( (2, 5) \).

So the correct response is:

(2, 5)