To determine the equation that represents the proportional relationship between the number of beats, [tex]\( b \)[/tex], and the length of the song, [tex]\( m \)[/tex], in minutes, let's break down the information given:
1. We know that there are 292 beats in 2 minutes of the song.
2. We need to find the relationship between beats and minutes.
Starting from the given data:
- There are [tex]\(292\)[/tex] beats for [tex]\(2\)[/tex] minutes.
First, let's calculate the number of beats per minute. We can do this by dividing the total number of beats by the total number of minutes:
[tex]\[ \text{beats per minute} = \frac{292 \text{ beats}}{2 \text{ minutes}} \][/tex]
[tex]\[ \text{beats per minute} = 146 \text{ beats per minute} \][/tex]
This tells us that for every minute, there are [tex]\(146\)[/tex] beats.
Next, we can express the relationship with an equation. Since the number of beats per minute is constant, the number of beats [tex]\( b \)[/tex] is directly proportional to the number of minutes [tex]\( m \)[/tex]. Therefore, we can write:
[tex]\[ b = 146m \][/tex]
This equation indicates that the number of beats [tex]\( b \)[/tex] is 146 times the number of minutes [tex]\( m \)[/tex].
Therefore, the correct equation representing the proportional relationship between the number of beats [tex]\( b \)[/tex] and the length of the song in minutes [tex]\( m \)[/tex] is:
[tex]\[ b = 146m \][/tex]
