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{ = }(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{ = }(1200-1600)/(4-0) \\ =\text{ }(-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}`