Think of "number of booklets" as $b$ and "total cost" as $C(b)$. Use the two pieces of information to form two points $(b, C(b))$ on a line.

Use the two points to compute the slope: slope $=$ (change in cost) ÷ (change in number of booklets). This gives you the cost per booklet.

Once you know the cost per booklet, plug it and one of the points into $C(b) = (\text{cost per booklet})\cdot b + (\text{fixed fee})$ and solve for the fixed fee, then compare with the answer choices.

In the first expression line, type (1780-660)/(400-120) and look at the value Desmos displays. That value is the cost per booklet (the slope).

Look at the number in front of $b$ in each answer choice. Keep only the choices whose coefficient of $b$ matches the slope value you just found in Desmos.

For each remaining choice, type it in Desmos exactly as written. Then either:

• Use a table in Desmos (click the gear and add a table) and enter $b=120$ and $b=400$, or
• Directly evaluate the function at those $b$-values. The correct choice will be the one that gives $660 when $b=120$ and $1,780 when $b=400$.

You can also plot the two points $(120,660)$ and $(400,1780)$ in Desmos (using a table) and see which line from the answer choices passes exactly through both points.

The total cost depends on the number of booklets, so think of the function as $C(b)$, where $b$ is the number of booklets.

From the problem:

• 120 booklets cost $660, corresponding to the point $(120,660)$
• 400 booklets cost $1,780, corresponding to the point $(400,1780)$

These are two points on the line $C(b)$.

The cost per booklet is the slope $m$ of the line through the two points.

Compute the slope:

• Change in cost: $1780 - 660 = 1120$
• Change in booklets: $400 - 120 = 280$

So the slope is

$m = 1120 / 280 = 4$.

That means each booklet costs $4$ dollars.

The function has the form $C(b) = 4b + f$, where $f$ is the fixed design fee.

Use one of the points, say $(120,660)$:

$660 = 4(120) + f$

$660 = 480 + f$

$f = 660 - 480 = 180$.

So the design fee is $180$ dollars.

Now substitute both the per-booklet cost and the design fee into the linear model:

$C(b) = 4b + 180$.

This matches answer choice D.