Question

nicole 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?
liters
(b) choose the statement that best describes how the time and amount of water are related. then fill in the blank.
○ as time increases, the amount of water in the tank decreases:
at what rate is the amount of water decreasing?
liters per minute
○ as time increases, the amount of water in the tank increases:
at what rate is the amount of water increasing?
liters per minute

Explanation:

Part (a)

Step 1: Identify the y - intercept

The graph shows the relationship between time (in minutes) and the amount of water (in liters). At time \(x = 0\) minutes (the y - intercept), we look at the value of the amount of water. From the graph, when \(x = 0\), the amount of water is 140 liters.

Part (b)

Step 1: Determine the relationship direction

Looking at the graph, as time (x - value) increases, the amount of water (y - value) is increasing (since the line has a positive slope). So we choose the statement "As time increases, the amount of water in the tank increases".

Step 2: Calculate the rate of increase

To find the rate of increase, we can use the slope formula. Let's take two points. At \(x = 0\), \(y=140\). Let's assume another point, for example, if we look at the grid, when \(x = 1\), let's see the change in \(y\). From the graph, the slope (rate of change) can be calculated. The difference in \(y\) over the difference in \(x\). Let's take two points: \((0,140)\) and \((1, 160)\) (assuming the grid lines, since from 140, each grid line might be an increase of 20? Wait, maybe better to see the vertical change. Wait, the y - axis: 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300? Wait, no, the labels: 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300? Wait, the first point is (0,140), and then when x increases by 1, y increases by 20? Wait, let's check the slope. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \(x_1 = 0,y_1 = 140\) and \(x_2=1,y_2 = 160\). Then \(m=\frac{160 - 140}{1 - 0}=\frac{20}{1}=20\). So the rate of increase is 20 liters per minute.

Answer:

(a) 140 liters
(b) The statement "As time increases, the amount of water in the tank increases" is correct. The rate of increase is 20 liters per minute.