To determine the ratio where the constant of proportionality appears based on the table, we need to examine the relationship between the amounts of raspberry and lemonade.
From the data table:
- When there is 1 scoop of raspberry, there are 2.5 cups of lemonade: (1, 2.5)
- When there are 2 scoops of raspberry, there are 5 cups of lemonade: (2, 5)
- When there are 4 scoops of raspberry, there are 10 cups of lemonade: (4, 10)
- When there are 6 scoops of raspberry, there are 15 cups of lemonade: (6, 15)
Since Rosie will use 2 scoops of raspberry to every 5 cups of lemonade, this ratio can be represented as (2, 5).
Now, looking at the other options, we can check the ratios:
- (1, 2.5) shows a 1:2.5 ratio which is proportional.
- (5, 2) does not reflect the relationship defined in the table since it reverses the order.
- (2, 5) is the ratio that Rosie plans to use and is also represented in the data table.
- (1, 2.5) is another valid point from the table representing the same proportion.
The constant of proportionality is identified by choosing the pairs of quantities that maintain the same ratio. In this case, the ratio of raspberry to lemonade Rosie's recipe presents is also observed in the data table entry (2, 5).
Thus, the correct answer for the ratio where the constant of proportionality appears is:
(2, 5).
2 answers