To determine which equation can be used to represent the number of public service announcements, [tex]\( y \)[/tex], in [tex]\( x \)[/tex] hours, let's analyze each option step by step:
1. [tex]\( y = \frac{x}{4} \)[/tex]
- This equation implies that the number of announcements increases slowly compared to the number of hours. Specifically, the number of announcements is one-fourth the number of hours. For example, in 4 hours, there would be only 1 announcement. This doesn't seem realistic for a scenario with frequent announcements.
2. [tex]\( y = 4 \)[/tex]
- This equation suggests that regardless of how many hours pass, the number of announcements remains constant at 4. This implies no correlation between [tex]\( y \)[/tex] and [tex]\( x \)[/tex], which is unlikely for a scenario where the number of announcements should vary with the number of hours.
3. [tex]\( y = 4x \)[/tex]
- This equation indicates a direct proportionality between the number of announcements and the number of hours. If [tex]\( x \)[/tex] doubles, [tex]\( y \)[/tex] also doubles. For instance, in 1 hour, there would be 4 announcements; in 2 hours, there would be 8 announcements, and so on. This seems like a logical way to model a situation where announcements are made periodically.
4. [tex]\( y = x + 4 \)[/tex]
- This equation suggests a linear relationship with a starting point of 4 announcements and an additional announcement for each passing hour. For example, if [tex]\( x \)[/tex] is 0, there are already 4 announcements, which may not always be realistic in a typical setting.
Among these options, the equation that most realistically and appropriately represents the number of public service announcements made in [tex]\( x \)[/tex] hours is [tex]\( y = 4x \)[/tex]. This is because it provides a clear and direct relationship where the number of announcements is a multiple of the number of hours, fitting well with the idea of periodic announcements.
Therefore, the correct option is:
[tex]\[ y = 4x \][/tex]
Index of the correct option is 3 (considering the list is 0-indexed).
