To analyze the given linear equation \( y = 1.5x + 12 \), we can identify the components of the equation:
- \( y \) represents the height of the water in the pool in inches.
- \( x \) represents the time in minutes after Daphne has begun pouring water.
- The coefficient of \( x \), which is 1.5, represents the rate at which the height of the water increases per minute.
- The constant term (12) represents the initial height of the water in the pool when \( x = 0 \).
Now, let's evaluate the statements:
-
Daphne has been pouring water for 12 minutes.
This statement is incorrect because there's no indication from the equation that Daphne has been pouring water for exactly 12 minutes. -
Daphne is pouring water into the pool at a rate of 12 inches per minute.
This statement is incorrect because the rate is 1.5 inches per minute, not 12 inches per minute. -
The height of the water in the pool is increasing at a rate of 1.5 inches per minute.
This statement is correct, as the coefficient of \( x \) (1.5) indicates the rate of increase in height per minute. -
The height of the water in the pool was 1.5 inches when Daphne started pouring water.
This statement is incorrect. When \( x = 0 \), the height of the water \( y \) is \( 1.5(0) + 12 = 12 \) inches, not 1.5 inches.
Therefore, the true statement based on the linear model is:
The height of the water in the pool is increasing at a rate of 1.5 inches per minute.