Use the image to answer the question.

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

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

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

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

(3.5, 6.5)

Answer 1

To estimate when the two divers are at the same depth, we need to look for the point where their heights (y-values) are the same. Based on the options given:

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

The point that indicates both divers being at the same depth should have the same y-coordinate (height) for both divers. The points (3.67, −7), (3, −6), and (3.5, −6.5) all have negative y-values, which suggests depths beneath the surface. However, (3.5, 6.5) represents a positive height, indicating a position above the pool edge, and thus does not approximate them being at the same depth.

Among the options given, (3.5, −6.5) is the most reasonable estimate, indicating a common depth of -6.5 feet at around 3.5 minutes after the buzzer.

Therefore, the best estimate is (3.5, −6.5).