Answer :
To solve this question, let's analyze the information provided:
1. We are given a table that shows the height of water in a pool over time as it is being filled. The table is presented with the relationship between time (in minutes) and height (in inches).
2. The points provided in the table are:
- At 2 minutes, the height is 8 inches.
- At 4 minutes, the height is 12 inches.
- At 6 minutes, the height is 16 inches.
- At 8 minutes, the height is 20 inches.
- At 10 minutes, the height is 24 inches.
3. We know that the slope of the line passing through these points is 2.
4. The slope of a line in the context of this problem indicates the rate of change of the height of the water with respect to time.
To understand the relationship between the slope and the height of the water, let's recall what a slope signifies. The slope \( m \) of a line given by the points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the following formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, \( x \) represents time (in minutes), and \( y \) represents the height of water (in inches). The given slope of 2 implies:
[tex]\[ \frac{\text{Change in Height}}{\text{Change in Time}} = \frac{y_2 - y_1}{x_2 - x_1} = 2 \][/tex]
This tells us that for every 1 minute increase in time, the height of the water increases by 2 inches.
Now, let's analyze the provided statements:
- "The height of the water increases 2 inches per minute." This statement correctly describes the relationship indicated by the slope. It means that for every minute, the water level rises by 2 inches, consistent with the given slope of 2.
- "The height of the water decreases 2 inches per minute." This is incorrect because the slope is positive, indicating an increase, not a decrease.
- "The height of the water was 2 inches before any water was added." This is incorrect because the slope describes the rate of change, not the initial condition. The initial condition is not provided in the slope context.
- "The height of the water will be 2 inches when the pool is filled." This is incorrect for the same reason as above; the slope does not relate to the final height.
Therefore, the correct statement is:
"The height of the water increases 2 inches per minute."
1. We are given a table that shows the height of water in a pool over time as it is being filled. The table is presented with the relationship between time (in minutes) and height (in inches).
2. The points provided in the table are:
- At 2 minutes, the height is 8 inches.
- At 4 minutes, the height is 12 inches.
- At 6 minutes, the height is 16 inches.
- At 8 minutes, the height is 20 inches.
- At 10 minutes, the height is 24 inches.
3. We know that the slope of the line passing through these points is 2.
4. The slope of a line in the context of this problem indicates the rate of change of the height of the water with respect to time.
To understand the relationship between the slope and the height of the water, let's recall what a slope signifies. The slope \( m \) of a line given by the points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the following formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, \( x \) represents time (in minutes), and \( y \) represents the height of water (in inches). The given slope of 2 implies:
[tex]\[ \frac{\text{Change in Height}}{\text{Change in Time}} = \frac{y_2 - y_1}{x_2 - x_1} = 2 \][/tex]
This tells us that for every 1 minute increase in time, the height of the water increases by 2 inches.
Now, let's analyze the provided statements:
- "The height of the water increases 2 inches per minute." This statement correctly describes the relationship indicated by the slope. It means that for every minute, the water level rises by 2 inches, consistent with the given slope of 2.
- "The height of the water decreases 2 inches per minute." This is incorrect because the slope is positive, indicating an increase, not a decrease.
- "The height of the water was 2 inches before any water was added." This is incorrect because the slope describes the rate of change, not the initial condition. The initial condition is not provided in the slope context.
- "The height of the water will be 2 inches when the pool is filled." This is incorrect for the same reason as above; the slope does not relate to the final height.
Therefore, the correct statement is:
"The height of the water increases 2 inches per minute."
