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 (710-230)/(26*60-8*60) to compute the rate of change in liters per second. Note the decimal value Desmos gives you for the slope.

In the next line, type b = 230 - (previous_answer)*480, where previous_answer is the slope value from step 1 (you can just retype the expression or copy it). Desmos will show you the value of b, the starting amount of water.

Use the slope from step 1 and the intercept from step 2 to write a linear equation of the form p(t) = (slope)*t + (intercept) in Desmos (for example, y = (slope)*x + (intercept)) and confirm it passes through both points (480,230) and (1560,710). Then choose the answer option whose equation has 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 $p(t)=\dfrac{4}{9}t+\dfrac{50}{3}$.