To determine the correct slope for the graph representing the remaining balance after each payment on Barton’s car loan, we can analyze the situation mathematically.
Barton’s car loan amount is $2,625, and he makes monthly payments of $175. The slope in this context represents the rate at which the remaining balance decreases with each payment made.
- Slope Calculation:
- The loan amount is decreasing by $175 each month as he makes his payments.
- Therefore, the slope can be represented as the change in the remaining balance over the change in time (months).
The formula for slope \( m \) is: \[ m = \frac{\text{change in y}}{\text{change in x}} = \frac{-175}{1} = -175 \]
- Interpretation:
- The negative sign indicates that the remaining balance is decreasing.
- Each month, the remaining balance decreases by $175.
Thus, the correct example that models the slope of the graph representing the remaining balance after each payment is:
Slope = -175
This implies that for every month that passes (or payment made), the remaining balance decreases by $175.
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