a. The constant of proportionality is k = 2.75.
b. Completing the Table:
Cups of Coffee (x) Total Cost (y)
1 $2.75
2 $5.50
3 $8.25
4 $11.00
5 2.75 * 5 = $13.75
6 2.75 * 6 = $16.50
c. The total cost increases by $2.75 for every additional cup of coffee purchased.
- The rate of change describes how one quantity changes in relation to the other quantity.
- In a proportional relationship, the rate of change is equal to the constant of proportionality, k.
Analyzing the Proportional Price Relationship:
a. Constant of Proportionality:
We need a data point to determine the constant of proportionality (k). The provided information includes two data points:
1 cup - $2.75
2 cups - $5.50
Using either data point, we can calculate k:
Method 1:
Substitute the first data point into the equation y = kx:
2.75 = k * 1
k = 2.75
Method 2:
Divide the cost for 2 cups by the number of cups:
5.50 / 2 = 2.75
k = 2.75
Therefore, the constant of proportionality is k = 2.75.
b. Finding Missing Prices:
Knowing the constant of proportionality allows us to find the missing prices on the menu. For any number of cups (x), we can calculate the total cost (y) using the formula:
y = 2.75x
Simply multiply the number of cups by the constant of proportionality.
Completing the Table:
Cups of Coffee (x) Total Cost (y)
1 $2.75
2 $5.50
3 2.75 * 3 = $8.25
4 2.75 * 4 = $11.00
5 2.75 * 5 = $13.75
6 2.75 * 6 = $16.50
7 2.75 * 7 = $19.25
8 2.75 * 8 = $22.00
9 2.75 * 9 = $24.75
10 2.75 * 10 = $27.50
c. Cost Change with Increasing Cups:
As the number of cups increases by 1, the total cost also increases proportionally by a constant amount. This constant amount is equal to the constant of proportionality, k = $2.75.
Therefore, every time you order one additional cup of coffee, the total cost will increase by $2.75.
Increase in Cost:____
As the number of cups increases by 1, the total cost also increases proportionally by a constant amount. This constant amount is equal to the rate of change, which is $2.75.
Therefore, every time you order one additional cup of coffee, the total cost will increase by $2.75.
As the cups of coffee increase by 1, the total cost increases by $2.75 each time. The rate of change describes how one quantity changes in relation to the other quantity.
In a proportional relationship, the rate of change is equal to the constant of proportionality, k. In this case, the rate of change is $2.75, which is also the constant of proportionality.