Barton took out a car loan of $2,625. He makes monthly payments of $175. The graph represents the remaining balance after each payment. Which example models the correct slope?

To find the slope of the line that represents the remaining balance on the car loan after each monthly payment, we can use the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

In this situation, the start point is (0, 2625) and the end point is (15, 0).

Therefore, we can define our points as follows:

• Point 1: \((x_1, y_1) = (0, 2625)\)
• Point 2: \((x_2, y_2) = (15, 0)\)

Now, we will calculate the slope:

\[ m = \frac{0 - 2625}{15 - 0} = \frac{-2625}{15} = -175 \]

Now, let's analyze the provided options to see which one correctly represents the slope:

1. \(m = \frac{9 - 8}{1,050 - 1,225}\)
2. \(m = \frac{525 - 700}{11 - 12}\)
3. \(m = \frac{2,450 - 2,625}{0 - 1}\)
4. \(m = \frac{1,050 - 1,225}{9 - 8}\)

Now let's check the slopes in the options, aiming for \(m = -175\).

1. \(m = \frac{1}{-175} = -0.0057\) (Not a match)
2. \(m = \frac{-175}{-1} = 175\) (Not a match)
3. \(m = \frac{-175}{-1} = 175\) (Not a match)
4. \(m = \frac{-175}{1} = -175\) (This matches our calculated slope)

Thus, the correct response that models the appropriate slope is:

Option 4: \(m = \frac{1,050 - 1,225}{9 - 8}\)