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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=9−81,050−1,225 m equals Start Fraction 9 minus 8 over 1,050 minus 1,225 End Fraction m=2,450−2,6250−1 m equals Start Fraction 2,450 minus 2,625 over 0 minus 1 End Fraction m=525−70011−12 m equals Start Fraction 525 minus 700 over 11 minus 12 End Fraction m=1,050−1,2259−8 m equals Start Fraction 1,050 minus 1,225 over 9 minus 8 End Fraction

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To find the slope representing the change in the remaining balance after each payment, we can model the balance as a function of the number of payments made. In this case, Barton started with a car loan of $2,625, and he makes monthly payments of $175.

The formula for calculating the remaining balance after \( n \) payments can be approximated as:

\[ \text{Remaining Balance} = 2625 - 175n \]

Now, to find the slope \( m \) of the line representing the change in balance with each payment, we can look for the change in balance for a change in the number of payments.

Let's interpret the values given in the potential responses as follows (where the first element is the remaining balance after some payments, and the second element is the number of payments made):

  1. \( m = \frac{9 - 8}{1050 - 1225} \)
  2. \( m = \frac{2450 - 2625}{0 - 1} \)
  3. \( m = \frac{525 - 700}{11 - 12} \)
  4. \( m = \frac{1050 - 1225}{9 - 8} \)

We will evaluate each option to find the one that correctly calculates the slope based on the monthly payment of $175:

  1. \( m = \frac{9 - 8}{1050 - 1225} \) = \(\frac{1}{-175} = -\frac{1}{175}\) (negative slope).
  2. \( m = \frac{2450 - 2625}{0 - 1} = \frac{-175}{-1} = 175\) (this is actually the positive rate of payment).
  3. \( m = \frac{525 - 700}{11 - 12} = \frac{-175}{-1} = 175\) (same as above).
  4. \( m = \frac{1050 - 1225}{9 - 8} = \frac{-175}{1} = -175\) (which is the actual effective negative slope).

Thus, based on the context and the interpretation of slope:

The two relevant responses that yield the change consistent with the monthly payment of $175 are options 2 and 3, both resulting in a payment rate of effectively being $175.

However, usually, when we talk about the 'slope' of a line in reference to payments, it's negative, representing that the balance decreases. So if we assume "slope" here refers to how much balance decreases with each payment, we will choose the first response since it represents the decrease from the loan’s beginning (though it provides a tricky view).

But if we're strictly interpreting the slope as the amount paid off relative to changes, then consider options 2 or 3, both yielding a positive 175 in different contexts.

Choose based on requirement or specify in context:

Option 2 or 3 as amounts paid \(= -175\) based on a slope conceptualization of total debt decrease.