Use the image to answer the question.

Question

The graph models the swimming paths of two students, where x represents the time after a buzzer sounds and y represents height from the pool edge. One student dived into the pool from the edge of the pool 3 minutes before the buzzer went off. The second student dived into the pool from a board 4 feet above the ground right when the buzzer went off. Which of the following points can be used to best estimate the time when the divers are at the same depth?

(1 point)
Responses

(3, −6)
left parenthesis 3 comma negative 6 right parenthesis

(3.5, 6.5)
left parenthesis 3.5 comma 6.5 right parenthesis

(3.67, −7)
left parenthesis 3.67 comma negative 7 right parenthesis

(3.5, −6.5)

Answer 1

To determine the time when the two divers are at the same depth, we need to analyze the points given. The point where both divers are at the same depth will have the same y-coordinate value (depth) for two different times (x-coordinates).

Let's analyze the options given:

1. (3, -6): This point indicates that at 3 minutes after the buzzer, one diver is at -6 feet. This does not imply the other diver is at the same depth at this time.

2. (3.5, 6.5): This point indicates that at 3.5 minutes after the buzzer, one diver is at 6.5 feet, while the other is at a different depth; thus, it does not mean they are at the same depth.

3. (3.67, -7): This point indicates that at 3.67 minutes after the buzzer, one diver is at -7 feet. Again, we cannot conclude that both divers are at the same depth just from this point.

4. (3.5, -6.5): This point indicates that at 3.5 minutes after the buzzer, both divers would need to be at -6.5 feet. If the graph suggests that at this time, both divers are at equivalent depths, it would indicate they are at the same depth.

Based on the nature of the problem and the information given, (3.5, -6.5) is the best estimate of the time when both divers are at the same depth.