The amount of time required to download a song from Michael's computer to his music player is the same for each song he downloads.

Question

A linear model of this situation contains the values (144 , 115.2) and (214 , 171.2), where x represents the number of songs he wants to download to his music player, and y represents the total amount of time, in minutes, it will take him to download the songs.

What is the rate of change in this linear model?
A.
70 minutes per song
B.
0.8 of a minute per song
C.
0.4 of a minute per song
D.
1.6 minutes per song

Answer 1

To determine the rate of change in this linear model, we can calculate the slope of the line using the two points given: (144, 115.2) and (214, 171.2). The formula for the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting in the values from the points:

• \((x_1, y_1) = (144, 115.2)\)
• \((x_2, y_2) = (214, 171.2)\)

We get:

\[ \text{slope} = \frac{171.2 - 115.2}{214 - 144} \]

Calculating the differences:

\[ y_2 - y_1 = 171.2 - 115.2 = 56 \]

\[ x_2 - x_1 = 214 - 144 = 70 \]

Now substituting these values back into the slope formula:

\[ \text{slope} = \frac{56}{70} \]

To simplify:

\[ \text{slope} = \frac{56 \div 14}{70 \div 14} = \frac{4}{5} = 0.8 \]

Thus, the rate of change is 0.8 of a minute per song, which corresponds to option B.