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 .

Answer 1

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.

1. Between \(x = 0\) and \(x = 2\):
- Change in \(y\): \(16,000 - 20,000 = -4,000\)
- Change in \(x\): \(2 - 0 = 2\)
- Slope: \(\frac{-4,000}{2} = -2,000\)

2. Between \(x = 2\) and \(x = 4\):
- Change in \(y\): \(12,000 - 16,000 = -4,000\)
- Change in \(x\): \(4 - 2 = 2\)
- Slope: \(\frac{-4,000}{2} = -2,000\)

3. 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.