First find how much the cost increases when the weight goes from 3 to 7 pounds, and how many pounds that is. Then divide the change in cost by the change in weight.

Once you know the increase in cost per pound (the slope $m$), use $S(w) = mw + b$ and one of the known packages to find $b$. Then substitute $w = 12$ into the formula.

If you know the cost change per pound, you can also start from one known package (for example, 7 pounds) and add the correct amount for the extra pounds to get the 12‑pound cost directly.

In the first expression line, type m = (14.05 - 8.45) / (7 - 3) and press Enter. Desmos will display the numeric value of $m$, the cost increase per pound.

In a new line, type b = 8.45 - m * 3 and press Enter. This uses the 3‑pound package to solve for $b$ in $S(w) = mw + b$.

In another line, type m * 12 + b. The value that Desmos shows for this expression is the cost, in dollars, to ship a 12‑pound package.

The cost function $S(w)=mw+b$ is linear in the weight $w$.

The two given packages give you two points on this line:

• A 3‑pound package costs $8.45$: this is the point $(3, 8.45)$.
• A 7‑pound package costs $14.05$: this is the point $(7, 14.05)$.

We will use these two points to find the slope $m$ and then use that to find the cost for 12 pounds.

The slope $m$ is the change in cost divided by the change in weight:

Compute the numerator and denominator:

• $14.05 - 8.45 = 5.60$
• $7 - 3 = 4$

So

This means the cost increases by $1 for each additional pound.

Use one of the points in the equation $S(w)=mw+b$ to solve for $b$.

Using the 3‑pound package $(3, 8.45)$ and $m = 1.40$:

Compute $1.40(3)$:

So

The cost function is

Now plug $w = 12$ into $S(w) = 1.40w + 4.25$:

First compute $1.40(12)$:

Then add the fixed fee:

So the cost to ship a 12‑pound package is $1, which corresponds to choice B.