Question

a hole 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:

Step1: Solve part (a)

To find the amount of water at 0 minutes, we look at the y - intercept of the graph (where \(x = 0\)). From the graph, when \(x=0\) (time = 0 minutes), the \(y\) - value (amount of water) is 150 liters.

Step2: Solve part (b) - Determine the relationship

Looking at the graph, as the \(x\) - value (time) increases, the \(y\) - value (amount of water) also increases. So we choose the statement "As time increases, the amount of water in the tank increases."

Step3: Calculate the rate of increase

The rate of change (slope) of a linear graph is given by \(\frac{\Delta y}{\Delta x}\). We can take two points on the line. From the graph, when \(x = 0\), \(y=150\) and when \(x = 1\), let's assume the \(y\) - value is \(150 + r\) (where \(r\) is the rate). Looking at the graph, when \(x = 0\), \(y = 150\) and when \(x=1\), \(y = 200\)? Wait, no, looking at the grid, when \(x = 0\), \(y = 150\), when \(x = 1\), the \(y\) - value is \(150+50 = 200\)? Wait, no, let's check the difference between two points. Let's take \((0,150)\) and \((1,200)\)? Wait, no, the vertical axis: at \(x = 0\), \(y = 150\); at \(x = 1\), the line is at \(y=200\)? Wait, the vertical axis has marks at 150, 200, 250, 300, 350, 400, 450, 500. The horizontal axis is time in minutes. The slope is \(\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: \((0,150)\) and \((1,200)\) (wait, no, when \(x = 0\), \(y = 150\); when \(x = 1\), the \(y\) - coordinate is \(200\)? Wait, the distance between 150 and 200 is 50, and the distance between \(x = 0\) and \(x = 1\) is 1. So the slope is \(\frac{200 - 150}{1 - 0}=\frac{50}{1}=50\). Wait, but let's check another point. When \(x = 0\), \(y = 150\); when \(x = 2\), \(y = 250\). Then \(\frac{250 - 150}{2 - 0}=\frac{100}{2}=50\). So the rate of increase is 50 liters per minute.

Answer:

(a) \(\boldsymbol{150}\) liters
(b) The correct statement is "As time increases, the amount of water in the tank increases." and the rate of increase is \(\boldsymbol{50}\) liters per minute.