To determine the correct interpretation of the slope, we need to understand what each statement is indicating about the relationship between the two variables (time on the tightrope and number of people).
-
The time on the tightrope goes up about 5 minutes for every 9 people.
- This suggests that for every 9 additional people, the time increases by 5 minutes.
-
The time on the tightrope goes up about 9 minutes for every 5 people.
- This suggests that for every 5 additional people, the time increases by 9 minutes.
-
The time on the tightrope goes up by about 2 people per minute.
- This suggests that for every additional minute, the time increases by 2 people, which does not make sense in the context of the phrase "time on the tightrope."
-
The time on the tightrope goes up about 1 minute for every 1 person.
- This suggests that for each additional person, the time increases by 1 minute.
To effectively interpret the slope, a ratio of change in time over change in the number of people should be considered. Without more context about what the slope specifically means in the relationship (e.g., the actual numerical values of the slope), it's impossible to definitively say which one is correct. However, if the slope represents time per unit of people, you would likely want to select the interpretation that matches the output (minutes) for the input (people).
So, if the slope was something like 1:1 or 5:9 based on the context given, the interpretation would revolve around those values.
If the slope were \( \frac{5}{9} \), then the correct interpretation would be the first statement: The time on the tightrope goes up about 5 minutes for every 9 people.
If the slope were \( \frac{9}{5} \), the correct one would be the second statement.
So, to conclude accurately, we need the actual value of the slope in the context, which isn't provided here. If you have that, I can help you select the right interpretation.