To determine the term that describes the slope of the graph representing the data in the given table, we'll follow these steps:
1. Examine the given data:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time (min)} & \text{Water in Pool (gal)} \\
\hline
0 & 50 \\
\hline
1 & 44 \\
\hline
2 & 38 \\
\hline
3 & 32 \\
\hline
4 & 26 \\
\hline
5 & 20 \\
\hline
\end{array}
\][/tex]
2. Calculate the differences in water levels and times:
- From time 0 to time 1: [tex]\(44 - 50 = -6\)[/tex]
- From time 1 to time 2: [tex]\(38 - 44 = -6\)[/tex]
- From time 2 to time 3: [tex]\(32 - 38 = -6\)[/tex]
- From time 3 to time 4: [tex]\(26 - 32 = -6\)[/tex]
- From time 4 to time 5: [tex]\(20 - 26 = -6\)[/tex]
3. Calculate the slope for each interval:
[tex]\( \text{slope} = \frac{\text{change in water level}}{\text{change in time}} \)[/tex]
For all intervals:
[tex]\[
\frac{-6}{1} = -6.0
\][/tex]
4. Interpret the slope:
- The slopes are all equal to -6.0.
- Since all slopes are negative, this indicates that the water level in the pool decreases over time.
Since the slope is consistently negative across the entire time period, it can be described as negative.
[tex]\[
\begin{tabular}{l}
\hline
\multicolumn{1}{|c|}{$\hspace{0.3cm}$} $\checkmark$ negative \\
undefined \\
zero \\
positive \\
\hline
\end{tabular}
\][/tex]
Therefore, the slope of the line representing the volume of water in the pool over time is best described as negative.
