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?

To determine the constant of proportionality in Rosie's recipe for raspberry lemonade, we first need to look at the ratio of raspberry scoops to cups of lemonade.

According to the information given:

• For every 5 cups of lemonade, Rosie uses 2 scoops of raspberry.

We can express this as a ratio:

• The ratio of scoops of raspberry (R) to cups of lemonade (L) is 2:5.

To find the constant of proportionality \( k \), we can express this ratio as:

\[ k = \frac{R}{L} = \frac{2 \text{ scoops}}{5 \text{ cups}} \]

Thus, the constant of proportionality \( k \) in this case is:

\[ k = \frac{2}{5} \]

So, the ratio at which the constant of proportionality appears is \( \frac{2}{5} \) or \( 0.4 \).