Question

owners of a recreation area are adding water to a pond. the graph below shows the amount of water in the pond (in liters) versus the amount of time that water is added (in hours). use the graph to answer the questions. (a) how much does the amount of water increase for each hour that water is added? liters (b) what is the slope of the line?

Explanation:

Step1: Find two points on the line

From the graph, when \( x = 0 \) (time = 0 hours), \( y = 100 \) liters. When \( x = 1 \) (time = 1 hour), \( y = 400 \) liters (approximate from the graph's trend, or we can see the slope calculation). Wait, actually, let's check the intercept. At \( x = 0 \), \( y = 100 \). Let's take another point. Let's say when \( x = 2 \), what's \( y \)? From the graph, the line goes from (0,100) to, say, (1, 400)? Wait, no, maybe better to calculate the slope. The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points: (0, 100) and (1, 400)? Wait, no, looking at the y-axis, at x=0, y=100. At x=1, the y-value is 400? Wait, no, maybe the grid. Let's see, the y-axis has 100, 200, 300, 400, 500, etc. At x=0, y=100. At x=1, y=400? Wait, no, maybe the slope is (400 - 100)/(1 - 0)=300? Wait, no, maybe I misread. Wait, the graph: when time is 0 hours, water is 100 liters. When time is 1 hour, water is 400 liters? Wait, no, let's check the line. The line starts at (0,100) and goes up. Let's take x=0, y=100; x=1, y=400? Wait, no, maybe the correct points are (0,100) and (2, 700)? Wait, no, maybe the slope is 300 per hour. Wait, let's do it properly.

Wait, the problem is about the amount of water increase per hour, which is the slope. Let's take two points: (0, 100) and (1, 400)? Wait, no, maybe (0,100) and (1, 400) is wrong. Wait, looking at the y-axis, each grid is 100 liters. At x=0, y=100. At x=1, the line is at y=400? Wait, no, maybe the correct calculation: the y-intercept is 100 (when x=0, y=100). Let's take x=1, then y=400? So the change in y is 400 - 100 = 300, change in x is 1 - 0 = 1. So the slope (and the rate of increase) is 300 liters per hour.

Step2: Answer part (a)

The amount of water increase per hour is the slope, which we calculated as 300 liters per hour.

Step3: Answer part (b)

The slope of the line is the same as the rate of increase, so it's 300.

Answer:

(a) 300 liters
(b) 300