Use the image to answer the question.



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

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

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

To determine the point that best estimates when the divers are at the same depth, we need to find the intersection point of the two lines representing the paths of the divers on the graph.

From the description, we know:

  1. The first student (diving from the edge of the pool) dived 3 minutes before the buzzer.
  2. The second student (diving from a board) started diving right when the buzzer went off and was 4 feet above the ground.

We are looking for a point (x, y) where both divers are at the same depth, meaning both paths intersect at that point.

Looking at the given options:

  • (3.5, 6.5)
  • (3.67, -7)
  • (3.5, -6.5)
  • (3, -6)

The depths (y-values) are negative, which usually indicates a depth under the pool surface.

To find the correct intersection point, we want a point where both x-values are reasonable given the time and the heights from their respective diving points.

Without the actual graph images, we can't specifically plot the values. But typically, the diver from the edge of the pool would reach the water quite quickly, while the one diving from the board would take a bit longer to reach the same depth.

Analyzing for depth:

  • (3.5, -6.5) has a reasonable value of -6.5 for depth.
  • (3, -6) also indicates a depth at -6 feet, which could make sense if they intersect around that time.

Both could represent reasonable intersection times, but the point (3.5, -6.5) might indicate a later intersection compared to (3, -6).

If we assume realistic diving depths and responses, it might be best to pick the point that indicates they meet at a reasonable depth rather than an extreme depth.

Thus, the point that can be used to best estimate the time when the divers are at the same depth would be:

(3.5, -6.5).