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), \( y = 600 \) liters (water in the pond). When \( x = 2 \) hours, \( y = 1400 \) liters.

Step2: Calculate the change in water and time

Change in water (\(\Delta y\)) = \( 1400 - 600 = 800 \) liters. Change in time (\(\Delta x\)) = \( 2 - 0 = 2 \) hours.

Step3: Find the rate of increase per hour

Rate = \(\frac{\Delta y}{\Delta x}=\frac{800}{2} = 400\) liters per hour.

Step1: Recall the formula for slope

The slope (\(m\)) of a line is given by \( m=\frac{\Delta y}{\Delta x} \), where \(\Delta y\) is the change in \( y \)-values and \(\Delta x\) is the change in \( x \)-values.

Step2: Use the points from part (a)

We can use the points \((0, 600)\) and \((2, 1400)\) (or any two points on the line). \(\Delta y = 1400 - 600 = 800\), \(\Delta x = 2 - 0 = 2\).

Step3: Calculate the slope

\( m=\frac{800}{2}=400 \). Also, since the line is linear and represents the rate of water increase, the slope is equal to the rate calculated in part (a).

Answer:

400

Part (b)