At time t=0 water begins to drip out of a pipe into an empty bucket. After 56 minutes 8 inches of water are in the bucket. What linear function in the form y=mx+b represents the amount of water in inches, w, in the bucket after t minutes

The linear function of the bucket is , where represents the amount of water, measured in inches, and is the time, measured in minutes.

Step-by-step explanation:

According to the Euclidean and Analytical Geometries, we can construct a line by knowing two distinct points on a plane. Besides, we know two different conditions for the bucket:

Initial condition of the bucket

Final condition of the bucket

The equation of the line is defined by the following model:

(1)

Where:

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

- y-Intercept, dimensionless.

- Slope, dimensionless.

Based on the known conditions of the bucket, we obtain the following system of linear equations:

(2)

(3)

The solution of the system of equations is:

and

Then, the linear function of the bucket is , where represents the amount of water, measured in inches, and is the time, measured in minutes.