To determine the correct slope modeling the remaining balance of Barton's car loan after each payment, we first need to understand what the slope represents in this context. The slope (m) will represent the change in the remaining balance of the loan per change in the number of payments made.
Given the information:
- Barton took out a car loan of $2,625.
- His monthly payments are $175.
After each payment, the remaining balance will decrease by the amount of the payment. Therefore, we can determine the slope based on the change in remaining balance and the change in the number of payments.
To analyze each option:
-
m = (525 - 700) / (11 - 12)
This is essentially calculating a change in balance over a change in payments, but since the values (525 and 700) are not directly related to the loan, this doesn't seem to model the situation correctly. -
m = (1,050 - 1,225) / (9 - 8)
Similar analysis; again, the numbers do not appear to relate properly to the loan payments or balances. -
m = (9 - 8) / (1,050 - 1,225)
The numerator (1) implies a change of 1 payment, while the denominator implies a change of -175 (since 1,050 - 1,225 = -175). This could represent a single payment and suggests the remaining balance decreasing due to a payment. This setup seems more in line with the idea that the remaining balance decreases by the monthly payment amount. -
m = (2,450 - 2,025) / (0 - 1)
Here, the numerator gives 425 and considers 1 payment (since 0 - 1 = -1). 425 divided by -1 would indicate how the balance changes over a payment. The values are more related to example payments, and this could also represent a decrease but does not maintain the context across payments accurately.
Calculating the slope for the remaining balance would focus mainly on the change derived from payments, which is, generally speaking, should be a fixed value, relating to the decrease in balance as it correlates to each month.
Given that a car loan payment usually has a straightforward relationship where each payment decreases the balance directly—you are seeking a model that properly adheres to that factor:
If we analyze closer but simplifying based on their description, a properly derived slope that might diagnose change is what usually reflects monthly repayment, equating to $175—or in solving sería a type of ratio concerning payments made.
Therefore, m = (2,450 - 2,025) / (0 - 1) looks the most promising as it conceptually aligns with the principle of loans. The negative sign simply shows a decrease, which is what should happen with each payment made—which can also be solved further, matching balance with precise figures against the remaining statements of other candidates.
Thus, although each paves boundary and could likely yield balance terms upon payment details, it can be this model reflecting each month properly tallying down.
Final answer: m = (2,450 - 2,025) / (0 - 1) is representative for the decline in balance caused by payments.
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