Question

changed during his dive.
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.
describe the rate of change for this relationship.
the amount of air in barrys tank decreased by 20 cubic feet per minute.
\\(\frac{1}{4}\\) of a cubic foot
\\(\frac{1}{2}\\) of a cubic foot
\\(1\frac{1}{4}\\) cubic feet

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 \( \frac{30 - 80}{40 - 0}=\frac{- 50}{40}=-\frac{5}{4}=-1\frac{1}{4} \). The negative sign indicates a decrease. So the amount of air decreases by \( 1\frac{1}{4} \) cubic feet per minute.

Answer:

The amount of air in Barry's tank decreased by \( 1\frac{1}{4} \) cubic feet per minute.