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=525−70011−12
𝑚
=
525
−
700
11
−
12
m equals Start Fraction 525 minus 700 over 11 minus 12 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=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=1,050−1,2259−8

Answer 1

To determine the correct slope that models the remaining balance of Barton’s car loan, we need to understand that the slope (m) can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

In this context, \(y\) represents the remaining balance and \(x\) represents the number of payments made.

Given the information:

1. Initially, Barton's loan amount is $2,625.
2. After one payment of $175, his remaining balance would be \(2,625 - 175 = 2,450\).
3. After two payments of $175, his remaining balance would be \(2,450 - 175 = 2,275\), and so on.

Next, let's analyze each option to see if they provide a correct slope that reflects the decrease in loan balance per payment.

1. **Option 1**: \( m = \frac{525 - 700}{11 - 12} \)
- This simplifies to \( m = \frac{-175}{-1} = 175 \), which does not correspond with the loan decrease, because the balance decreases not increases.

2. **Option 2**: \( m = \frac{9 - 8}{1,050 - 1,225} \)
- This simplifies to \( m = \frac{1}{-175} \), which does not make sense in the context of remaining balances.

3. **Option 3**: \( m = \frac{2,450 - 2,625}{0 - 1} \)
- This simplifies to \( m = \frac{-175}{-1} = 175 \), which correctly indicates an increase in balance, hence not the right model for a loan.

4. **Option 4**: \( m = \frac{1,050 - 1,225}{9 - 8} \)
- This simplifies to \( m = \frac{-175}{1} = -175\). This indicates that with every payment, the loan decreases by $175, which correctly models the remaining balance of the loan.

Thus, the correct example that models the slope of the remaining balance after each payment is **Option 4**:

\[ m = \frac{1,050 - 1,225}{9 - 8} \]