Question

Use the graph to answer the 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.

Answer 1

To find the rate of change of the DVD player's resale value over time based on the points given, we can use the formula for the slope of a line, which is:

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

From the points provided:
- \( (0, 300) \) represents the value of the DVD player at time 0 years (original purchase).
- \( (4, 0) \) represents the value of the DVD player at time 4 years.

Using these points, we can calculate the slope:

\[
y_1 = 300, \quad y_2 = 0, \quad x_1 = 0, \quad x_2 = 4
\]

Now, plug in the values:

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

This means the rate of change is \(-75\), indicating that the value drops $75 every year.

So, the correct response is:

–75; The value drops $75 every year.