To determine the correct slope for Barton’s car loan scenario, we need to consider the definition of slope in the context of his loan payments.
The slope \( m \) is computed using the formula:
\[ m = \frac{\text{change in } y}{\text{change in } x} \]
In this case, \( y \) represents the remaining balance of the loan, and \( x \) represents the number of payments made.
Given:
- He took out a car loan of $2,625.
- After each payment of $175, the remaining balance decreases.
The remaining balance after one payment can be represented as:
- After 1 payment: \( 2,625 - 175 \)
- After 2 payments: \( 2,625 - 2 \cdot 175 \)
The slope represents the rate of change of the balance with respect to the number of payments made. For each payment made, the balance decreases by $175.
Let's evaluate each provided example to find which expression reflects the correct slope:
-
\( m = \frac{1,050 - 1,225}{9 - 8} \)
- Here, the change in balance seems not to match the payment structure correctly.
-
\( m = \frac{9 - 8}{1,050 - 1,225} \)
- This essentially results in a very small number and does not represent the payment structure.
-
\( m = \frac{525 - 700}{11 - 12} \)
- Again, this doesn't match the decreasing balance by $175 correctly.
-
\( m = \frac{2,450 - 2,625}{0 - 1} \)
- This results in \( \frac{-175}{-1} = 175 \), which is the amount by which the balance decreases after each payment.
Therefore, the correct example that models the correct slope is:
\( m = \frac{2,450 - 2,625}{0 - 1} \).
1 answer