To determine the slope represented by the graph of the remaining balance after Barton's monthly payments, we need to establish what the slope represents.
In this context:
- The slope \( m \) represents the change in the remaining loan balance (in dollars) over the change in time (in months). Since Barton is making monthly payments of $175, we would expect the slope to represent a decrease in the remaining balance.
The slope can be calculated using the formula:
\[ m = \frac{\text{change in } y}{\text{change in } x} \]
Given that for each month (1 month later), the balance decreases by $175:
- The line moves down by 175 dollars for each increase of 1 month.
Now let's analyze the options provided:
A. \( m = \frac{2450 - 2625}{0 - 1} \)
This represents the change in balance from \( 2625 \) at month \( 0 \) to \( 2450 \) at month \( 1 \):
\[ m = \frac{-175}{-1} = 175 \]
B. \( m = \frac{525 - 700}{11 - 12} \)
This represents a change in balance from \( 700 \) at month \( 12 \) to \( 525 \) at month \( 11 \):
\[ m = \frac{-175}{-1} = 175 \]
C. \( m = \frac{1050 - 1225}{9 - 8} \)
This represents a change in balance from \( 1225 \) at month \( 8 \) to \( 1050 \) at month \( 9 \):
\[ m = \frac{-175}{1} = -175 \]
D. \( m = \frac{9 - 8}{1050 - 1225} \)
This represents a reverse calculation that does not accurately reflect the balance change:
\[ m = \frac{1}{-175} = -\frac{1}{175} \]
Both options A and B yield a correct slope of 175, which represents the correct change in balance for each month.
Thus, both A and B model the correct slope.
If you need to choose a single option, then either one would be acceptable as they are both accurate in representing the decrease in loan balance per month. To select only one, A is sufficient as it clearly illustrates the calculation for the first month. However, B is also valid for an understanding of how the next month relates.