A bakery is making loaves of French bread. The recipe calls for 2 cups of flour per loaf of bread. The data table shows how much flour the bakery needs depending on the number of loaves it intends to make. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.
The constant of proportionality appears as the ratio between the number of loaves of bread and the amount of flour needed. So, looking at the data table, we can find this ratio by dividing the amount of flour needed by the number of loaves for each row.
For example, for the row 2 loaves - 4 cups, the ratio is 4 cups / 2 loaves = 2 cups/loaf.
Similarly, for the row 4 loaves - 8 cups, the ratio is 8 cups / 4 loaves = 2 cups/loaf.
We can continue this for each row and see that the ratio remains constant at 2 cups/loaf.
Therefore, the constant of proportionality appears as the ratio (2, 1) in the data table.
To determine the ratio at which the constant of proportionality appears in the data table, we need to find two entries in the table where the input and output values are directly proportional.
Given that the recipe calls for 2 cups of flour per loaf of bread, we can calculate the amount of flour needed for each number of loaves in the data table.
Data Table:
Number of Loaves | Cups of Flour
1 | 2
2 | 4
3 | 6
4 | 8
By looking at the data table, we can observe that as the number of loaves increases by 1, the cups of flour increase by 2.
Therefore, the constant of proportionality appears at the ratio of (1, 2).
To find the constant of proportionality in a proportional relationship, we need to find the ratio between the two related quantities.
First, let's look at the data table to determine the ratio between the number of loaves and the amount of flour needed:
Number of Loaves (x) | Cups of Flour (y)
------------------------------------------
1 | 2
2 | 4
3 | 6
4 | 8
To find the ratio, we can divide the number of cups of flour by the number of loaves for each row of the table:
For the first row:
2 cups of flour ÷ 1 loaf = 2 cups of flour per loaf
For the second row:
4 cups of flour ÷ 2 loaves = 2 cups of flour per loaf
For the third row:
6 cups of flour ÷ 3 loaves = 2 cups of flour per loaf
For the fourth row:
8 cups of flour ÷ 4 loaves = 2 cups of flour per loaf
As we can see, the ratio is always 2 cups of flour per loaf, regardless of the number of loaves. Therefore, the constant of proportionality is 2.
In the data table, the ratio where the constant of proportionality appears is represented by the ordered pair (x, y) = (1, 2).