Question

In the table, x represents how many years Ms. Wilson has owned her car, and y represents the value of the car.

Years, x - Value in Dollars, y
0 - $20,000
2 - $16,000
4 - $12,000
8 - $4,000

The slope of the function is _ because as the time Ms.Wilson has owned her car _, the value in dollars _.

Answer 1

To find the slope of the function that relates the years Ms. Wilson has owned her car to the value of the car, we can look at the change in value per year.

Using the two data points (0, $20,000) and (8, $4,000), we can calculate the slope \( m \):

1. **Calculate the change in value (y)**:
\[
\Delta y = y_2 - y_1 = 4,000 - 20,000 = -16,000
\]

2. **Calculate the change in years (x)**:
\[
\Delta x = x_2 - x_1 = 8 - 0 = 8
\]

3. **Calculate the slope (\( m \))**:
\[
m = \frac{\Delta y}{\Delta x} = \frac{-16,000}{8} = -2,000
\]

So the slope of the function is \(-2,000\).

Now, we can complete the sentence:

The slope of the function is **-2,000** because as the time Ms. Wilson has owned her car **increases**, the value in dollars **decreases**.