To understand how the slope relates to the height of the water in the pool, we first need to understand what the slope represents in this context. The slope is a measure of the rate of change of the height of the water with respect to time.
In our table, the pairs of values represent the time in minutes and the corresponding height in inches of water in the pool. Examining the data:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time (min)} & \text{Height (in.)} \\
\hline
2 & 8 \\
\hline
4 & 12 \\
\hline
6 & 16 \\
\hline
8 & 20 \\
\hline
10 & 24 \\
\hline
\end{array}
\][/tex]
- At 2 minutes, the height is 8 inches.
- At 4 minutes, the height is 12 inches.
- At 6 minutes, the height is 16 inches.
- At 8 minutes, the height is 20 inches.
- At 10 minutes, the height is 24 inches.
We observe that for every 2-minute increment in time, the height of the water increases by 4 inches. This can be formally described by finding the slope ([tex]\(m\)[/tex]) of the line passing through these points. The slope is given by the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{\text{change in height}}{\text{change in time}}
\][/tex]
Using any two points from the table:
[tex]\[
m = \frac{12 - 8}{4 - 2} = \frac{4}{2} = 2
\][/tex]
So, the slope is [tex]\(2\)[/tex]. This means that for each minute, the height of the water increases by 2 inches (as slopes can be interpreted as the change in [tex]\( y \)[/tex] (height) per unit change in [tex]\( x \)[/tex] (time)).
Therefore, the correct statement that describes how the slope relates to the height of the water in the pool is:
The height of the water increases 2 inches per minute.
