To determine how the slope of the line relates to the height of the water in the pool, let's follow these step-by-step steps:
1. Interpret the Data Given in the Table:
- At time = 2 minutes, the height of the water is 8 inches.
- At time = 4 minutes, the height of the water is 12 inches.
- At time = 6 minutes, the height of the water is 16 inches.
- At time = 8 minutes, the height of the water is 20 inches.
- At time = 10 minutes, the height of the water is 24 inches.
2. Define the Concept of Slope:
- The slope of a line in the context of a word problem typically represents a rate of change.
- It tells us how much one quantity (the height of the water) changes on average with respect to another quantity (time).
3. Calculate the Slope:
- The slope ([tex]\(m\)[/tex]) can be calculated using the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x}
\][/tex]
Here, [tex]\(\Delta y\)[/tex] represents the change in height, and [tex]\(\Delta x\)[/tex] represents the change in time.
4. Verify the Slope:
- Looking at the table, for every 2 minutes, the height of the water increases by 4 inches.
- If we calculate the slope using two points, say [tex]\((2, 8)\)[/tex] and [tex]\((4, 12)\)[/tex]:
[tex]\[
m = \frac{12 - 8}{4 - 2} = \frac{4}{2} = 2
\][/tex]
- Similarly, this rate of change, 2, is consistent between any pair of points in this data set.
5. Interpret the Slope:
- The calculated slope is 2. This slope gives us the rate at which the height of the water in the pool is increasing.
6. Choose the Correct Interpretation:
- The statement “The height of the water increases 2 inches per minute.” correctly describes the situation represented by the table and the slope of 2.
- Other options like the height decreasing, the initial height, or the final height when the pool is filled either don't match our slope calculation or are inaccurately linked to the given slope value.
Therefore, the correct statement is:
- "The height of the water increases 2 inches per minute."
