Question

lucia is downloading songs to make a playlist for her quinceañera. the graph shows the time in minutes, y, as a function of the number of songs downloaded, x. the initial value of the function is 12. the rate of change is 1.5. what does the rate of change represent? the number of songs lucia can download each minute the time in minutes it takes each song to download the number of songs lucia already downloaded

Explanation:

The rate of change in a linear function \( y = mx + b \) (where \( y \) is time in minutes and \( x \) is number of songs) represents the change in \( y \) per unit change in \( x \). Here, \( y \) is time and \( x \) is number of songs, so the rate of change (slope \( m = 1.5 \)) means the time (in minutes) it takes to download each song. Let's analyze the options:

• "the number of songs Lucia can download each minute" would be \( \frac{1}{m} \) (songs per minute), not \( m \) (minutes per song).
• "the time in minutes it takes each song to download" matches the interpretation of slope (change in time per change in number of songs, i.e., minutes per song).
• "the number of songs Lucia already downloaded" is the initial value (when \( x = 0 \)), not the rate of change.

Answer:

the time in minutes it takes each song to download