Question

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?
the start point is (0,2625)
and the end point is (15,0)
(1 point)
Responses

m=9−8/1,050−1,225
m equals Start Fraction 9 minus 8 over 1,050 minus 1,225 End Fraction

m=525−700/11−12
m equals Start Fraction 525 minus 700 over 11 minus 12 End Fraction

m=2,450−2,625/0−1
m equals Start Fraction 2,450 minus 2,625 over 0 minus 1 End Fraction

m=1,050−1,225/9−8
m equals Start Fraction 1,050 minus 1,225 over 9 minus 8 End Fraction

Answer 1

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