Once you have the times in seconds, think of the situation as a line passing through two points $(t,p(t))$. What are these two points, and how do you find the slope between them?

After you find the slope (rate of change), plug the slope and one point into $p(t)=mt+b$ to solve for $b$. Then write the full equation and compare it to the answer choices.

In one expression line, type m=(710-230)/(26*60-8*60) to define the filling rate in liters per second. Desmos will show that $m=\frac{4}{9}$.

In the next line, type b=230-m*(8*60). This uses the point $(480,230)$ and the slope you defined to find the starting amount of water.

Type y=m*x+b and enter the points (480,230) and (1560,710) on separate lines. Confirm that both points lie on the line, then choose the answer option with the same slope and intercept.

The problem defines $t$ as seconds, but the data are given in minutes.

• After $8$ minutes, $t=8\times 60=480$ seconds, and the amount is $230$ liters.
• After $26$ minutes, $t=26\times 60=1560$ seconds, and the amount is $710$ liters.

So we have two points on the line: $(480,230)$ and $(1560,710)$, where the first coordinate is time in seconds and the second is liters.

For a linear function $p(t)=mt+b$, the slope $m$ is the rate of change:

Now simplify $\frac{480}{1080}$ by dividing top and bottom by $120$:

So the tank is filling at $\frac{4}{9}$ liters per second.

Use $p(t)=mt+b$ and substitute $m=\frac{4}{9}$ and one of the points, say $(480,230)$:

Compute $\frac{4}{9}\cdot 480$:

So

Convert $230$ to thirds: $230 = \frac{690}{3}$. Then

This $b$ is the amount of water in the tank at $t=0$ seconds.

Now plug the slope and intercept into $p(t)=mt+b$:

This matches choice D, so the correct equation is $p(t)=\dfrac{4}{9}t+\dfrac{50}{3}$.