Bot GPT 4-o mini To identify the correct slope that models the remaining balance after each payment, we need to analyze how the loan balances change over time with each payment.
The original loan amount is $2,625, and Barton makes monthly payments of $175. The remaining balance after each payment can be represented by taking the difference in the amount of the remaining balance and the time it takes (in months) to get that balance.
The slope (\(m\)) of a line is given by the formula:
\[ m = \frac{{\text{change in y}}}{{\text{change in x}}} \]
Where:
- Change in y is the change in the remaining balance.
- Change in x is the change in the number of payments (time in months).
Let's evaluate each of the provided responses to determine which one might represent the slope:
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Response 1: \[ m = \frac{9 - 8}{1,050 - 1,225} \quad \text{(Not related to loan amounts)} \]
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Response 2: \[ m = \frac{525 - 700}{11 - 12} \quad \text{(Not related to loan amounts)} \]
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Response 3: \[ m = \frac{2450 - 2625}{0 - 1} = \frac{-175}{-1} = 175 \]
- This reflects the monthly payment of $175, as the balance decreases by that amount each month.
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Response 4: \[ m = \frac{1050 - 122}{?} \quad \text{(Incomplete, cannot evaluate)} \]
Among these options, Response 3 correctly reflects the decrease in remaining balance with each monthly payment, indicating the slope of the line representing remaining balance over time. It confirms that for each month (1), the remaining balance decreases by $175.
Therefore, the correct model for the slope is: \[ m = \frac{2450 - 2625}{0 - 1} \]
1 answer