Use the two points from the bills to compute the slope $m = \dfrac{\text{change in cost}}{\text{change in pages}}$. Be careful to subtract in the same order in the numerator and denominator.

Write the relationship as $C = mp + b$ using the slope you found. Then substitute one of the points (either one) to set up an equation you can solve for $b$, the fixed monthly fee.

Once you know both the cost per page and the fixed fee, write the full equation and look for the answer choice with the same slope and the same constant term.

In Desmos, create a table. In the first column (x), enter 300 and 500. In the second column (y), enter 54 and 74. You will see the two points $(300, 54)$ and $(500, 74)$ plotted.

In a new expression line, type y = m x + b. Desmos will create sliders for $m$ and $b$. Adjust the sliders until the line passes exactly through both plotted points.

Once your line goes through both points, look at the values of $m$ (the slope) and $b$ (the y-intercept) from the sliders. Then choose the answer option whose equation has that same slope and constant term.

Because the total monthly charge $C$ is linearly related to the number of pages $p$, each billing situation can be seen as a point $(p, C)$.

• Last month: 300 pages cost $54, so one point is $(300, 54)$.
• This month: 500 pages cost $74, so another point is $(500, 74)$.

These two points lie on the line that represents the equation for $C$ in terms of $p$.

The slope $m$ of a line through $(x_1, y_1)$ and $(x_2, y_2)$ is

Here, use $(300, 54)$ and $(500, 74)$:

So the cost increases by $0.10 per extra page.

A linear relationship between $C$ and $p$ can be written as

where $m$ is the slope (cost per page) and $b$ is the fixed monthly fee.

You found $m = 0.10$, so the equation becomes

Now plug in one of the known points to solve for $b$. Using $(300, 54)$:

Subtract 30 from both sides to get $b$:

Now substitute $m = 0.10$ and $b = 24$ into the linear equation:

Check the answer choices and select the one that exactly matches this equation, which is $C = 0.10p + 24$. This is the correct equation for the total monthly charge in terms of $p$, the number of pages.