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Two intersecting lines are graphed across a coordinate plane.

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

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

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

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

(3.5, −6.5)

1 answer

To determine the point that best estimates when both divers are at the same depth, we need to consider the context of their diving paths.

  1. One student dove into the pool 3 minutes before the buzzer sounded, meaning they have already been in the water when the buzzer occurs.
  2. The second student dove from a height of 4 feet into the pool at the moment the buzzer went off.

The x-coordinates of the points represent time after the buzzer. So, we need to find where the y-coordinates are equal, which indicates that both divers are at the same depth below the surface of the water.

Reviewing the given points:

  • (3.5, 6.5): This indicates at 3.5 minutes after the buzzer, one diver is at a depth of 6.5 feet, while the other diver's position is not given.
  • (3.67, -7): Indicates one diver is at -7 feet at about 3.67 minutes after the buzzer.
  • (3, -6): Indicates one diver is at -6 feet at 3 minutes after the buzzer.
  • (3.5, -6.5): Indicates one diver is at -6.5 feet at 3.5 minutes after the buzzer.

Since we want to find when they are at the same depth, we should look for where both are at the same depth (y-value) at the same time (x-value). However, based on the context, it makes sense that they might be at negative depths, indicating being underwater.

Among these choices, (3, -6) suggests that at 3 minutes after the buzzer, both are at a depth of -6 feet, indicating they are at the same level underwater at that time.

Thus, the best estimate for when the divers are at the same depth is: (3, -6).