To determine the slope of the line that represents the relationship between time and the volume of water in the pool, we should use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
From the given table, we can extract the data points. Let's consider the first two points for simplicity:
- [tex]\((x_1, y_1) = (0, 50)\)[/tex]
- [tex]\((x_2, y_2) = (1, 44)\)[/tex]
Substitute the values into the slope formula:
[tex]\[ \text{slope} = \frac{44 - 50}{1 - 0} \][/tex]
[tex]\[ \text{slope} = \frac{-6}{1} \][/tex]
[tex]\[ \text{slope} = -6 \][/tex]
The slope is calculated as [tex]\(-6\)[/tex].
In terms of the characteristics of the slope:
- A positive slope means the line is increasing.
- A negative slope means the line is decreasing.
- A zero slope means the line is horizontal.
Since the slope found here is [tex]\(-6\)[/tex], it indicates that the line is decreasing. Therefore, the term that describes the slope of the line of a graph representing the data in the table is "negative".
Thus, the slope of a line graphed to represent the volume of water in a pool over time is described as negative.
