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:

Part (a)

Step1: Identify two points on the line

From the graph, we can see that when \( x = 0 \) (time = 0 hours), \( y = 200 \) liters (initial water). When \( x = 1 \) hour, \( y = 300 \) liters (water after 1 hour).

Step2: Calculate the increase in water per hour

The increase in water from \( x = 0 \) to \( x = 1 \) is \( 300 - 200 = 100 \) liters. So, the amount of water increases by 100 liters for each hour water is added.

Part (b)

Step1: Recall the formula for slope

The slope \( m \) of a line is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line.

Step2: Use the points from part (a)

Using \( (x_1,y_1)=(0,200) \) and \( (x_2,y_2)=(1,300) \), we substitute into the slope formula: \( m = \frac{300 - 200}{1 - 0}=\frac{100}{1}=100 \).

Answer:

s:
(a) 100
(b) 100