To accurately interpret the slope, we need to understand how the two variables in question are related.
Typically, if you have a slope with a ratio like \( \frac{9}{5} \), it means that for every increase of 5 in the independent variable (e.g., the number of people), the dependent variable (e.g., the time on the tightrope) increases by 9. This could be interpreted as:
- The time on the tightrope goes up by about 9 minutes for every 5 people.
If the slope were \( \frac{1}{1} \), it would mean that for every additional person, the time increases by 1 minute.
If the slope were \( \frac{5}{9} \), which is a reciprocal interpretation, it would mean that for every increase of 9 people, the time increases by 5 minutes.
Finally, if the interpretation was given as "2 people per minute," that would mean the slope is portrayed inversely, relating a change in time to a change in the number of people, which does not match the usual interpretation of slope.
Considering the statements provided, the first one seems most likely to correctly interpret the slope:
The time on the tightrope goes up about 9 minutes for every 5 people.
This choice accurately reflects a direct relationship where the dependent variable (time) increases as the independent variable (people) increases.
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