Question

Which statement correctly interprets the slope?

(1 point)
Responses

The time on the tightrope goes up about 9 minutes for every 5 people.
The time on the tightrope goes up about 9 minutes for every 5 people.

The time on the tightrope goes up about 1 minute for every 1 person.
The time on the tightrope goes up about 1 minute for every 1 person.

The time on the tightrope goes up about 5 minutes for every 9 people.
The time on the tightrope goes up about 5 minutes for every 9 people.

The time on the tightrope goes up by about 2 people per minute.

Answer 1

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.