Question

question
ariana 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 number of people in the music hall 1 hour after 6 p.m.
the average change in the number of hours since 6 p.m. for every additional person.
the number of hours past 6 p.m. when there is 1 person in the music hall.
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Explanation:

The line of best fit has \( x \)-axis as "Hours Past 6 p.m." and \( y \)-axis as "People Inside Music Hall". The slope of a line in a graph is \( \frac{\text{change in } y}{\text{change in } x} \). Here, \( y \) is the number of people and \( x \) is hours past 6 p.m. So slope represents the average change in \( y \) (number of people) for each unit change in \( x \) (each additional hour past 6 p.m.).

• The second option is incorrect because slope is change in people over change in hours, not vice versa.
• The third option is incorrect as slope is a rate of change, not the number of people at a specific hour (that would be a \( y \)-value at \( x = 1 \), not the slope).
• The fourth option is incorrect as slope is not about finding hours when there's 1 person (that would involve solving for \( x \) when \( y = 1 \), not slope interpretation).

Answer:

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