Question

A swimming pool is being filled. The graph shows the number of gallons $y$in the pool after $x$ minutes.

At what rate is the pool being filled?

Short answer

The pool is being filled at the rate of$15$ gallons per minute.

Step-by-step solution

Step 1. Slope formula.

If the graph of a linear function passes through the two points$\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, then the rate of change of the function is:

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

Step 2. Given information.

The given graph shows the number of gallons $y$in the pool after $x$minutes.

Step 3. Find the rate of change.

From the above graph it is clear that the line passes through the points$\left(0,20\right)$ and $\left(2,50\right)$.

Using the slope formula, the slope of the given graph is:

role="math" localid="1645091313339" $$\begin{gathered} m=\frac{50-20}{2-0} \\ =\frac{30}{2} \\ =15 \end{gathered}$$

The slope of the given graph is $15$.

In the graph, the $x$-axis represents the time (min) and the $y$-axis represents the volume of water (gallons).

Thus, the pool is being filled at the rate of$15$ gallons per minute.