Question

Barton took out a car loan of $2,625. He makes monthly payments of $175. The graph represents the remaining balance after each payment. Which example models the correct slope?

(1 point)
Responses

m=2,450−2,6250−1
𝑚
=
2
,
450
−
2
,
625
0
−
1
m equals Start Fraction 2,450 minus 2,625 over 0 minus 1 End Fraction

m=9−81,050−1,225
𝑚
=
9
−
8
1
,
050
−
1
,
225
m equals Start Fraction 9 minus 8 over 1,050 minus 1,225 End Fraction

m=525−70011−12
𝑚
=
525
−
700
11
−
12
m equals Start Fraction 525 minus 700 over 11 minus 12 End Fraction

m=1,050−1,2259−8

Answer 1

To find the correct slope that models the remaining balance of Barton’s car loan after each monthly payment, we need to determine the change in remaining balance over the change in number of payments.

In this case, Barton took out a loan of $2,625 and makes monthly payments of $175. The balance decreases with each payment.

1. Each payment reduces the balance by $175.
2. Therefore, the slope can be represented by \(\Delta y / \Delta x\), where \(\Delta y\) is the change in the remaining balance, and \(\Delta x\) is the change in the number of payments.

The general format for the slope, given the balance after \(n\) payments, can be derived as:

\[
m = \frac{\text{Remaining Balance after n payments} - \text{Remaining Balance after m payments}}{n - m}
\]

Now, looking at the options one by one:

1. \(m = \frac{2,450 - 2,625}{0 - 1}\): This calculates the change in balance as \(-175\) and a change in payments of \(-1\), which gives \(m = 175\).

2. \(m = \frac{9 - 8}{1,050 - 1,225}\): Here, the change in payments is \(1\) but the balance doesn’t align as it should reflect the actual loan balance of $2,625.

3. \(m = \frac{525 - 700}{11 - 12}\): This also does not match the payment amounts and remaining balance in context of the loan.

4. \(m = \frac{1,050 - 1,225}{9 - 8}\): This calculates a payment change of \(1\) and the balance change does not correspond correctly to the loan.

The first option is the only one that correctly reflects the loan payment of $175 decrease in the balance. Therefore, the correct model for the slope representing the remaining balance after each payment is:

**\(m = \frac{2,450 - 2,625}{0 - 1}\) which simplifies to 175.**

Thus, the slope that models the correct remaining balance is:
\[
m = 175\text{ (for each payment)}
\]