Final answer:
The constant of proportionality is the ratio of two related quantities that remains constant, such as the $2.50 per call in a donation job scenario, or a slope of 0.25 representing the trade-off between bus tickets and burgers.
Step-by-step explanation:
When we talk about a $$ off sale at Bettie’s Boutique, we are usually dealing with a linear relationship between the amount spent and the discount received, which involves finding the constant of proportionality. This concept is essential in understanding direct variation where one quantity varies directly as another. To find the constant of proportionality, you take the ratio of the two related quantities, which remains constant.
In the example of your job calling for donations, the pay (p) you receive is directly proportional to the number of calls (n) you make, such that p = A × n, where A represents the constant of proportionality. If you are paid $2.50 for each call, then A is $2.50, indicating that for every call you make, you earn $2.50.
Similarly, for other situations like the opportunity cost of goods, the constant of proportionality is found by taking the ratio of the two items' prices. For instance, the slope of the trade-off between bus tickets and burgers is calculated by dividing the price of bus tickets by the price of burgers ($0.50/$2), which equals 0.25. Thus, the constant ratio here is 0.25, meaning that each bus ticket is worth the opportunity cost of a quarter of a burger.