Question

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

Answer 1

Answer:

The linear function of the bucket is $y = \frac{1}{7}\cdot x$, where $y$ represents the amount of water, measured in inches, and $x$ 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

$A(x,y) = (0\,min, 0\,in)$

Final condition of the bucket

$B(x,y) = (56\,min, 8 in)$

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

$y = m\cdot x + b$ (1)

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$b$ - y-Intercept, dimensionless.

$m$ - Slope, dimensionless.

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

$b = 0$ (2)

$56\cdot m +b = 8$ (3)

The solution of the system of equations is:

$m = \frac{1}{7}$ and $b = 0$

Then, the linear function of the bucket is $y = \frac{1}{7}\cdot x$, where $y$ represents the amount of water, measured in inches, and $x$ is the time, measured in minutes.