Question

1. barry went scuba diving on his family vacation. the amount of air in his tank steadily changed during his dive.
2. there is a linear relationship between the time, in minutes, that barry was diving, and the amount of air in his tank, in cubic feet.

(chart: x-axis time (minutes) from 0 to 40, y-axis air in tank (cubic feet) from 10 to 100, line from (0,80) to (40,30))

1. describe the rate of change for this relationship.
2. the amount of air in barrys tank dropdown by dropdown per minute.

Explanation:

Step1: Identify two points

From the graph, when \( x = 0 \) (time = 0 minutes), \( y = 80 \) cubic feet. When \( x = 40 \) (time = 40 minutes), \( y = 30 \) cubic feet.

Step2: Calculate rate of change

The rate of change (slope) of a linear relationship is given by \( \frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points \((0, 80)\) and \((40, 30)\), we get \( \frac{30 - 80}{40 - 0}=\frac{- 50}{40}=-1.25 \). The negative sign indicates the amount of air is decreasing.

Answer:

The amount of air in Barry's tank decreases by \( 1.25 \) cubic feet per minute.