Question

A swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour. The depth of the water after 5 hours is 32 inches. Write the equation for this function in point slope form

Answer 1

Answer:

The equation in point slope form is $y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)$

Step-by-step explanation:

Since the swimming pool is being drained at a constant rate, the equation of the process must be a first-order polynomial (linear function), where depth of water decrease as time goes by. The form of the expression is:

$y = m \cdot t + b$

Where:

$t$ - Time, measured in hours.

$b$ - Initial depth of the water in swimming pool (slope), measured in inches.

$m$ - Draining rate, measured in inches per hour.

$y$ - Current depth of the water in swimming pool (x-Intercept), measured in inches.

If $m = -3\,\frac{in}{h}$ and $y (5\,h) = 32\,in$, the initial depth of the water in swimming pool is:

$b = y - m\cdot t$

$b = 32\,in -\left(-3\,\frac{in}{h} \right)\cdot (5\,h)$

$b = 47\,in$

The equation in point slope form is:

$y-y_{o} = m \cdot (t-t_{o})$

Where $y_{o}$ and $t_{o}$ are initial depth of the water in swimming pool and initial time, respectively. Then, the equation in point slope form is:

$y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)$