Question

A graph titled Resale Value of DVD Player is shown. The vertical axis represents the DVD player's value in dollars; the horizontal axis represents the number of years after original purchase. A line passes through the points left parenthesis 0 comma 300 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
Find the rate of change.

(1 point)
Responses

–75
; The value drops $75 every year.

– 75 ; The value drops $75 every year.

–150/4
; The value drops $150 every 4 years.

– 150 / 4 ; The value drops $150 every 4 years.

–4
; The value drops $4 every year.

– 4 ; The value drops $4 every year.

–1
; The value drops $1 every year.

– 1 ; The value drops $1 every year.

Answer 1

To find the rate of change of the resale value of the DVD player, we need to calculate the slope of the line that passes through the given points (0, 300) and (4, 0).

The formula for the slope (rate of change) is:

\[
\text{slope} = \frac{\text{change in value}}{\text{change in time}} = \frac{y_2 - y_1}{x_2 - x_1}
\]

In this case:
- \((x_1, y_1) = (0, 300)\)
- \((x_2, y_2) = (4, 0)\)

Now we can plug the values into the formula:

\[
\text{slope} = \frac{0 - 300}{4 - 0} = \frac{-300}{4} = -75
\]

This means the rate of change of the value of the DVD player is \(-75\).

Thus, the correct response is:

–75; The value drops $75 every year.