Question

The x-axis ranges from negative 10 to 10 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1. The dotted line is labeled 3 x plus y equals 4. It passes through the approximate points left parenthesis 0 comma 4 right parenthesis, left parenthesis 3.5 comma negative 6.5 right parenthesis, and left parenthesis 4.3 comma negative 9 right parenthesis. The solid line is labeled x plus y equals negative 3. It passes through the approximate points left parenthesis 0 comma 4 right parenthesis, left parenthesis 3.5 comma negative 6.5 right parenthesis, and left parenthesis 5.5 comma negative 8.5 right parenthesis.
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)
(3.5, - 6.5)
(3.5, 6.5)
(3, - 6)
(3.67, - 7)

Answer 1

They are at the same depth where the two lines intersect. Solve
3x + y = 4
x + y = −3
Subtract: 2x = 7 → x = 3.5. Then y = −3 − 3.5 = −6.5.

So (3.5, −6.5).