Question

the table shows the height of water in a pool as it is being filled.
height of water in a pool

time (min)	height (in.)
4	12
6	16
8	20
10	24

the slope of the line through the points is 2. which statement describes how the slope relates to the height of the water in the pool?

• the height of the water increases 2 inches per minute.
• the height of the water decreases 2 inches per minute.
• the height of the water was 2 inches before any water was added.
• the height of the water will be 2 inches when the pool is filled.

Explanation:

Step1: Recall slope formula

Slope \( m=\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1} \), where \( \Delta y \) is change in height (inches) and \( \Delta x \) is change in time (minutes).

Step2: Calculate slope from table

Take two points, e.g., \( (2,8) \) and \( (4,12) \).
\( \Delta y = 12 - 8 = 4 \), \( \Delta x = 4 - 2 = 2 \).
Slope \( m=\frac{4}{2}=2 \).
This means for each 1 - minute increase in time, height increases by 2 inches (since \( \frac{\Delta \text{height}}{\Delta \text{time}} = 2 \)).

Step3: Analyze options

• Option 1: Matches the slope interpretation (height increases 2 inches per minute).
• Option 2: Slope is positive, so height increases, not decreases. Eliminate.
• Option 3: The y - intercept (initial height) is found by \( y=mx + b \). Using \( (2,8) \) and \( m = 2 \), \( 8=2(2)+b\Rightarrow b = 4 \), so initial height is 4, not 2. Eliminate.
• Option 4: Slope relates to rate of change, not final height. Eliminate.

Answer:

The height of the water increases 2 inches per minute.