Question

A 1600 gallon pool is being drained. It is being drained at a rate of 50 gallons per hour. I have put everything in the table and graphed it and answered the questions, I just need help with the equation.

Answer 1

The equation representing the real-world scenario is linear as shown io the graph.

Generally, a linear equation takes the form:

$\begin{gathered} y\text{ =mx + c} \\ \text{where m is the slope} \\ c\text{ is the intercept} \end{gathered}$

The slope (m) is calculated using the formula:

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$

On the line, we have the points: (0, 1600), (4, 1200)

Substituting we have:

$\begin{gathered} m\text{ = }\frac{1200-1600}{4-0} \\ =\text{ }\frac{-400}{4} \\ =\text{ -100} \end{gathered}$

The y-intercept is the value of the y-axis when the line cuts the y-axis

y-intercept : (0, 1600)

Hence, the equation is:

$y\text{ = -100x + 1600}$