To find the correct slope that represents Barton's car loan payments, we need to consider the change in the remaining balance after each payment.
Barton took out a car loan of $2,625 and pays $175 per month. Thus, for each month, the remaining balance decreases by $175.
The slope \( m \) in the context of the graph represents the change in amount (y-axis) over the change in months (x-axis). Since the balance decreases by $175 each month, we can express this slope mathematically as:
\[ m = \frac{{\text{Change in Amount}}}{{\text{Change in Months}}} = \frac{{\text{Old Balance} - \text{New Balance}}}{{\text{Old Month} - \text{New Month}}} \]
Now, let's analyze the options provided to see which one correctly models this relationship:
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Option 1: \( m = \frac{525 - 700}{11 - 12} \)
- This represents a negative slope over an interval of 1 month.
- It's not directly related to the loan payment of $175.
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Option 2: \( m = \frac{2,450 - 2,625}{0 - 1} \)
- This calculates as \( m = \frac{-175}{-1} = 175 \), which equals the payment amount. This represents a one-month change correctly.
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Option 3: \( m = \frac{1,050 - 1,225}{9 - 8} \)
- This calculates as \( m = \frac{-175}{1} = -175 \), which correctly represents the decrease in balance but gives a negative slope.
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Option 4: \( m = \frac{9 - 8}{1,050 - 1,225} \)
- This represents a non-relevant ratio and does not make sense for the context of the payments.
Given that we need the slope that reflects the regular payment and decrease in balance due to the loan:
The correct answer is Option 2: \[ m = \frac{2,450 - 2,625}{0 - 1} \] This correctly models the slope of $175 increase in payments over 1 month.