To determine the slope of the line that represents the volume of water in a pool over time, we use the concept of the rate of change. The slope of the line can be calculated using two coordinate points from the data given in the table.
Given data points:
- Time (minutes): [tex]\(0, 1, 2, 3, 4, 5\)[/tex]
- Water in Pool (gallons): [tex]\(50, 44, 38, 32, 26, 20\)[/tex]
To calculate the slope ([tex]\(m\)[/tex]), we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's choose the points [tex]\((0, 50)\)[/tex] and [tex]\((1, 44)\)[/tex] for our calculation.
Here, [tex]\(x_1 = 0\)[/tex], [tex]\(y_1 = 50\)[/tex], [tex]\(x_2 = 1\)[/tex], and [tex]\(y_2 = 44\)[/tex].
Substitute these values into the formula:
[tex]\[ m = \frac{44 - 50}{1 - 0} \][/tex]
[tex]\[ m = \frac{-6}{1} \][/tex]
[tex]\[ m = -6 \][/tex]
Thus, the slope of the line that represents the volume of water in the pool over time is [tex]\(-6\)[/tex]. This means that for every minute that passes, the volume of water in the pool decreases by 6 gallons.
Therefore, the slope of a line graphed to represent the volume of water in a pool over time would be described as [tex]\(-6\)[/tex].
