To understand how the slope relates to the height of the water in the pool, we'll examine the time and height data and determine what the slope represents in this context.
The given table shows the time (in minutes) and the corresponding height (in inches) of the water in a pool:
| Time (min) | Height (inches) |
|------------|-----------------|
| 2 | 8 |
| 4 | 12 |
| 6 | 16 |
| 8 | 20 |
| 10 | 24 |
The slope of the line through the points in the table is given as 2.
To interpret what this slope means, let's first recall that the slope in a linear relationship [tex]\( y = mx + b \)[/tex] represents the rate of change of the dependent variable (height, in this case) with respect to the independent variable (time).
Here’s a step-by-step explanation:
1. Identify two points on the line:
For instance, let's use the points (2, 8) and (4, 12).
2. Slope Formula:
The slope [tex]\( m \)[/tex] is calculated as:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Plug in the values:
Using the points (2, 8) and (4, 12):
[tex]\[
m = \frac{12 - 8}{4 - 2} = \frac{4}{2} = 2
\][/tex]
This shows that the slope is indeed 2.
4. Interpret the Slope:
The slope of 2 indicates that for every minute that passes, the height of the water in the pool increases by 2 inches.
Therefore, the correct statement describing how the slope relates to the height of the water in the pool is:
The height of the water increases 2 inches per minute.
