Question

austin is filling a tank. the graph shows the amount of water (in liters) in the tank versus time (in minutes).
(a) what is the amount of water in the tank at 0 minutes?
\boxed{} liters
(b) choose the statement that best describes how the time and amount of water are related. then fill in the blank.
circ as time increases, the amount of water in the tank decreases.
at what rate is the amount of water decreasing?
\boxed{} liters per minute
circ as time increases, the amount of water in the tank increases.
at what rate is the amount of water increasing?
\boxed{} liters per minute

Explanation:

Step1: Analyze part (a)

To find the amount of water at 0 minutes, we look at the y - intercept of the graph. The y - axis represents the amount of water (in liters) and the x - axis represents time (in minutes). At \(x = 0\) (0 minutes), we check the value on the y - axis. From the graph, when \(t=0\) (time = 0 minutes), the amount of water is 200 liters (since the line starts at (0, 200)).

Step2: Analyze part (b)

We observe the trend of the graph. As time (x - value) increases, the amount of water (y - value) is increasing (since the line has a positive slope, going from left to right, it is rising). So the statement is "As time increases, the amount of water in the tank increases."

Step3: Analyze the rate of increase

To find the rate of increase (slope of the line), we can use two points on the line. Let's take two points: \((0,200)\) and let's assume another point. From the graph, if we look at the grid, when \(x = 4\) minutes, let's see the y - value. Wait, maybe we can calculate the slope. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \((0,200)\) and suppose at \(x = 4\) minutes, the y - value is, say, 400? Wait, no, looking at the graph, the line goes from (0,200) and let's see the next point. Wait, maybe the grid: the y - axis has marks like 200, 300, 400, 500, 600, 700, 800. The x - axis has 0,1,2,3,4,5,6,7,8,9. Let's take two points: (0, 200) and (4, 400)? Wait, no, maybe (0,200) and (8, 600). Then the slope \(m=\frac{600 - 200}{8 - 0}=\frac{400}{8}=50\) liters per minute. Wait, let's check again. If at \(x = 0\), \(y = 200\); at \(x = 4\), \(y = 400\), then slope \(m=\frac{400 - 200}{4 - 0}=\frac{200}{4}=50\) liters per minute. So the rate of increase is 50 liters per minute.

Answer:

(a) 200 liters
(b) As time increases, the amount of water in the tank increases.
Rate of increase: 50 liters per minute