In the table, x represents how many years Ms. Wilson has owned her car, and y represents the value of the car. Cost of a Pack of Baseball Cards Years, x Value in Dollars, y 0 $20,000 2 $16,000 4 $12,000 8 $4,000 (3 points) The slope of the function is because as the time Ms. Wilson has owned her car , the value in dollars .

Question

In the table, x represents how many years Ms. Wilson has owned her car, and y represents the value of the car. Cost of a Pack of Baseball Cards Years, x Value in Dollars, y 0 $20,000 2 $16,000 4 $12,000 8 $4,000   (3 points) The slope of the function is  because as the time Ms. Wilson has owned her car , the value in dollars .

GPT-4o mini · Answer

To find the slope of the function, we need to calculate the change in value ($y$) over the change in years ($x$).

From the data provided:

At $x = 0$, $y = 20,000$
At $x = 2$, $y = 16,000$
At $x = 4$, $y = 12,000$
At $x = 8$, $y = 4,000$

Let's calculate the slope between two points to establish a general trend.

Between $x = 0$ and $x = 2$:
- Change in $y$: $16,000 - 20,000 = -4,000$
- Change in $x$: $2 - 0 = 2$
- Slope: $\frac{-4,000}{2} = -2,000$
Between $x = 2$ and $x = 4$:
- Change in $y$: $12,000 - 16,000 = -4,000$
- Change in $x$: $4 - 2 = 2$
- Slope: $\frac{-4,000}{2} = -2,000$
Between $x = 4$ and $x = 8$:
- Change in $y$: $4,000 - 12,000 = -8,000$
- Change in $x$: $8 - 4 = 4$
- Slope: $\frac{-8,000}{4} = -2,000$

The slope is consistent in all cases at $-2,000$.

So, we can fill in 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 by $2,000 for each year.