To find the correct slope that models the remaining balance after each payment for Barton's car loan, we need to identify how the remaining balance changes with each payment.
Let's analyze the options provided:
-
m = (1,050 - 1,224) / (9 - 8): This equation is not a good model for the slope since it does not relate to the context of the car loan balance after a payment.
-
m = (2,450 - 2,625) / (0 - 1): This also seems inaccurate; the values 2,450 and 2,625 do not seem related to the payments made.
-
m = (525 - 700) / (11 - 12): Similar issue; it's unclear how these values directly relate to the payments or balance.
-
m = (9 - 8) / (1,050 - 1,225): This option appears to also be not relevant.
Analyzing the loan for Barton, starting with a balance of $2,625 and making payments of $175 per month:
After \( n \) months, his remaining balance can be calculated using the formula:
\[ \text{Remaining Balance} = 2,625 - 175n \]
To find the slope (m), we consider two points for the linear relationship which is the balance after two specific payments. For example, if after 1 month his balance is:
After 1 month:
- Remaining balance = 2,625 - 175(1) = 2,450
- This means for point (0, 2,625) to (1, 2,450).
So the slope between these two points:
\[ m = \frac{2,450 - 2,625}{1 - 0} = \frac{-175}{1} = -175 \]
This slope indicates a decrease in the balance by $175 for each payment made.
Thus, none of the provided options properly reflect the slope of the situation described regarding Barton's loan balance changes.
1 answer