Use the table to answer the question.

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

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

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

(1, 2.5)

Answer 1

To find the constant of proportionality in the given table, we look for the ratio of raspberry to lemonade at each point. The constant of proportionality can be found by dividing the amount of raspberry by the amount of lemonade.

From the table given:

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

All of these ratios simplify to 0.4, indicating that the amount of raspberry and lemonade maintains a proportional relationship.

To find the right coordinate pair that indicates the constant of proportionality in the context of the original question, we need the ratio where the first number represents raspberry and the second number represents lemonade.

In the context of the responses provided, the correct choice for the coordinate that yields the ratio of raspberry to lemonade directly from the table is:

(1, 2.5)

Thus, the answer is (1, 2.5).