Question

Which of the following statements are true regarding Sheila's scenario? Select all that apply:

1. If Sheila has a remaining balance of $2,000, the anticipated number of payments she would have made is 40 payments.
2. The y-intercept in this scenario stands for the remaining balance at the time of purchase.
3. The y-intercept in this scenario stands for the number of payments made.
4. If Sheila has a remaining balance of $2,000, the anticipated number of payments she would have made is 60 payments.
5. If Sheila has a remaining balance of $3,000, the anticipated number of payments she would have made is 50 payments.

Answer 1

Without explicit details of Sheila's scenario, we look to analogous examples to understand that the y-intercept typically represents a starting value, while the slope reflects the rate of change. Examples from tutoring fees and intertemporal budget constraints illustrate these concepts.

Step-by-step explanation:

To answer these questions, we need to understand the concepts of linear equations and the relationship between the slope and the y-intercept. The given information about Sheila's scenario is lacking to determine the exact numbers of payments, so we will rely on provided examples that are relevant to understanding linear equations.

The y-intercept corresponds to the initial value before any changes occur as a result of the slope. For instance, in a financial context, the y-intercept can represent the starting balance or one-time fee at the beginning of a payment plan. On the other hand, the slope reflects the rate of change in the variable of interest. In economics, a slope can indicate the rate at which future value increases due to the interest rate over time, or how each additional unit affects the total cost in a payment plan.

We can see the relevance of these concepts in Svetlana's tutoring sessions where the y-intercept (a = 25) represents a one-time fee charged at the beginning, and the slope (b = 15) indicates the ongoing hourly charge for her service. Similarly, Yelberton's scenario reflects how changes in the interest rate impact the slope of an intertemporal budget constraint, affecting the potential future value of current savings.