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

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

(3.67, −7)

1 answer

To determine which point best estimates the time when both divers are at the same depth, we want to look for a point where the y-coordinates (representing depth) are equal and correspond correctly to the x-coordinates representing the time since the buzzer sounded.

Given the parameters:

  • The first diver (3 minutes before the buzzer) would have a negative depth since they are already in the water.
  • The second diver (diving as the buzzer sounds) starts from 4 feet above the water.

Let's analyze each option:

  1. (3.5, 6.5): Here, the depth is positive, suggesting the diver is above the water, which isn't possible for both divers at the same depth.

  2. (3, −6): This indicates that the first diver is 6 feet underwater at 3 minutes after the buzzer, while the second diver isn't at that time (consistently above the ground initially).

  3. (3.5, −6.5): This indicates a depth of 6.5 feet for the first diver, which could be plausible as he has been underwater longer since diving before the buzzer. If the second diver (diving at the buzzer) also reaches this depth at a similar timeline, it could be a candidate.

  4. (3.67, −7): Similarly, this depth indicates the first diver would be at 7 feet underwater. This could also match if the second diver is now at the same depth.

Since we want the best estimate for when both divers are at the same depth, (3.5, −6.5) and (3.67, −7) are the candidates where they are both represented as being underwater.

Based on these assessments:

  • If they are indeed at the same depth at that time, (3.5, −6.5) is likely the best estimate as it provides a specific time clearly marked for the first diver.

So the answer is: (3.5, −6.5).