Use the given water usages for 2005 and 2018 to create two points of the form $(p, W)$ that lie on the line.

Use the slope formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ with your two points. Think about whether the slope should be positive or negative based on the context.

Once you know the slope and the value of $W$ when $p=0$, plug them into $W(p)=mp+b$ and then look for the choice that has both that slope and that intercept.

In Desmos, type (0,12.4) and (13,8.3) on separate lines so both points appear on the coordinate plane. Remember: $p=0$ for 2005 and $p=13$ for 2018.

On a new line, type (8.3-12.4)/(13-0) and look at the value Desmos gives. This is the slope (rate of change in millions of gallons per year). Compare this number to the coefficients of $p$ in the answer choices.

Notice from the problem and from the plotted point that when $p=0$, $W=12.4$, so the y-intercept must be 12.4. Choose the answer choice whose coefficient of $p$ matches the slope you found in Desmos and whose constant term is 12.4.

Let $p$ be the number of years after 2005, and let $W(p)$ be the water usage in millions of gallons.

• In 2005, $p=0$ and $W=12.4$, so one point is $(0,12.4)$.
• In 2018, $p=2018-2005=13$, and $W=8.3$, so the second point is $(13,8.3)$.

For a linear function, the constant rate of change is the slope $m$.

Use the slope formula with the two points $(0,12.4)$ and $(13,8.3)$:

Now rewrite $-4.1$ as a fraction. Since $4.1=\frac{41}{10}$,

So the slope is $m=-\tfrac{41}{130}$.

The y-intercept $b$ is the value of $W$ when $p=0$.

From the problem, in 2005 (which is $p=0$), the water usage was 12.4 million gallons, so the intercept is

A linear function in slope-intercept form is $W(p)=mp+b$.

We found:

• Slope $m=-\tfrac{41}{130}$
• Intercept $b=12.4$

So the model is

This matches choice D.