Question

(c): your answer is incorrect. 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 water is in the pond at 0 hours?
liters (b) how much water is in the pond at 1 hour?
liters (c) how much does the amount of water increase for each hour that water is added?
liters (d) are the amounts given in parts (b) and (c) equal? why or why not? choose the best answer. yes, because the line passes through (0, 0). yes, because the line does not pass through (0, 0). no, because the line passes through (0, 0). no, because the line does not pass through (0, 0).

Explanation:

Part (a)

Step1: Identify x=0 on graph

At \( x = 0 \) (0 hours), the y - value (water in liters) is 200.

Step1: Find x=1 on graph

At \( x = 1 \) (1 hour), look at the graph. The line passes through (1, 300)? Wait, no, let's check the y - axis. Wait, the y - intercept is 200. Let's calculate the slope first? Wait, no, at x = 1, from the graph, when x = 0, y = 200; x = 1, let's see the rise. Wait, maybe the graph: when x = 0, y = 200; x = 1, y = 300? Wait, no, the y - axis: 200, 250, 300, 350, 400, 450, 500. The line starts at (0, 200) and goes up. Let's see the slope. Wait, for part (a), x=0, y=200. For part (b), x=1, so we look at the point where x = 1. From the graph, when x = 1, y = 300? Wait, no, maybe the grid: each x - unit is 1 hour, y - unit is 50 liters? Wait, no, the y - axis: 200, 250, 300, etc. Wait, the line passes through (0, 200) and let's see another point. Let's say at x = 2, y = 400? Wait, no, 200 to 400 in 2 hours? Then slope is (400 - 200)/2 = 100. Wait, maybe at x = 1, y = 300. So at x = 1, y = 300.

Step1: Locate x=1 on x - axis

Find the point on the line where \( x = 1 \). The y - coordinate (water) is 300.

Step1: Calculate slope (rate of increase)

Slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Use points (0, 200) and (1, 300). \( m=\frac{300 - 200}{1 - 0}=100 \). So the water increases by 100 liters per hour.

Step2: Verify with another point

Take (0, 200) and (2, 400). \( m=\frac{400 - 200}{2 - 0}=\frac{200}{2}=100 \). Consistent.

Answer:

200

Part (b)