Question

question
fawzia keeps track of the number of people inside a music hall to attend a concert by looking at the number of scanned tickets. she plotted the data on the graph below, where x = 0 represents the time at 6 p.m., then drew a line of best fit. what does the slope of the line represent?
answer
the average change in the number of people for every additional hour past 6 p.m.
the average change in the number of hours since 6 p.m. for every additional person.
the number of people in the music hall 1 hour after 6 p.m.
the number of hours past 6 p.m. when there is 1 person in the music hall.

Explanation:

The slope of a line in a graph represents the rate of change of the dependent variable with respect to the independent variable. Here, the independent variable \( x \) is hours past 6 p.m., and the dependent variable is the number of people in the music hall. So the slope represents the average change in the number of people for every additional hour past 6 p.m.

Let's analyze each option:

• "The average change in the number of hours since 6 p.m. for every additional person": This is incorrect because the slope should relate the change in people to the change in time, not the other way around.
• "The number of people in the music hall 1 hour after 6 p.m.": The slope is a rate of change, not a specific number of people at a particular time.
• "The number of hours past 6 p.m. when there is 1 person in the music hall": The slope is not about finding the time when there is a specific number of people, but about the rate of change of people with respect to time.
• "The average change in the number of people for every additional hour past 6 p.m.": This matches the definition of slope as the rate of change of the dependent variable (number of people) with respect to the independent variable (hours past 6 p.m.).

Answer:

The average change in the number of people for every additional hour past 6 p.m.