Treat the two quotes as two points: $(p, C) = (10000, 1500)$ and $(16000, 2100)$. Plug each into $C(p) = mp + b$ to form two equations in $m$ and $b$.

Once you have the two equations, subtract one from the other to eliminate $b$ and solve for the per-pound rate $m$. Then plug that value back into either equation to find $b$.

In Desmos, enter each answer choice as a separate function, for example:

• C_A(p) = 0.10p + 1000
• C_B(p) = 0.05p + 1000
• C_C(p) = 10p - 500
• C_D(p) = 0.10p + 500 (Desmos allows function names like C_A(p).)

Under the functions, type evaluations like C_A(10000), C_A(16000), C_B(10000), etc. Desmos will display the corresponding cost values for each function at 10,000 and 16,000 pounds.

Compare the outputs to the actual quotes, $1500$ and $2100$. The correct function is the one whose values at $p = 10000$ and $p = 16000$ both exactly match these two quoted costs.

Because the quote is a one-time truck rental fee plus a charge directly proportional to the weight, the cost as a function of weight is linear. Let

• $p$ = shipment weight in pounds
• $C(p)$ = quoted cost in dollars

The general form is

where $m$ is the cost per pound and $b$ is the fixed truck rental fee.

Plug each weight–cost pair into $C(p) = mp + b$:

• For 10,000 pounds and $1{,}500$ dollars:

• For 16,000 pounds and $2{,}100$ dollars:

So you have a system of two equations in $m$ and $b$:

$1500 = 10000m + b$ and $2100 = 16000m + b$.

Subtract the first equation from the second to eliminate $b$:

So

The company charges $0.10$ per pound.

Use one of the original equations to solve for $b$. Using $1500 = 10000m + b$ and $m = 0.10$:

So the cost function is

which matches choice D.