a swimming pool holds 30,000 gallons of water. the graph shown below represents the amount of water, in…

Explanation:

Step1: Find slope of the line

First, identify two points on the line: $(0, 30)$ (initial state, 0 minutes, 30 thousand gallons) and $(150, 15)$ (150 minutes, 15 thousand gallons). Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{15 - 30}{150 - 0} = \frac{-15}{150} = -0.1$

Step2: Write linear equation

Use the y-intercept $b=30$ (when $x=0$, $y=30$). The equation is $y = -0.1x + 30$, where $y$ is thousands of gallons, $x$ is minutes.

Step3: Solve for $x$ when $y=0$

Set $y=0$ (pool completely drained): $0 = -0.1x + 30$ $0.1x = 30$ $x = \frac{30}{0.1} = 300$

Answer:

B. 300