The cost that changes with the number of miles should be multiplied by $d$, the delivery distance. Which number in the problem should be multiplied by $d$?

The fixed fee should appear as a constant term added to the expression, not multiplied by $d$ and not inside parentheses with $d$.

Because Desmos usually uses $x$ and $y$, rewrite each choice with $x$ instead of $d$ and $y$ instead of $P$. For example, enter four functions: $y = 3x + 1.50$, $y = 1.50x + 3$, $y = x/1.50 + 3$, and $y = 1.50(x + 3)$.

For each function, tap the gear icon and create a table. Look at the $y$-value when $x = 0$. The correct model should have a $y$-value of 3 when $x = 0$, because the fixed service fee is $3 even at 0 miles.

In the same tables, compare the change in $y$ when $x$ increases from $0$ to $1$. The correct model will increase by $1.50 for each 1-mile increase, matching the $1.50 per mile description.

The problem describes two separate parts of the total price $P$:

• A fixed service fee of $3. This does not depend on distance.
• A charge of $1.50 per mile, which does depend on the delivery distance $d$.

So the total price is "fixed fee + (per-mile cost)."

A typical linear cost equation looks like

• $P = (\text{rate per mile}) \cdot d + (\text{fixed fee})$.

Here:

• The rate per mile is $1.50, so it should be the coefficient multiplied by $d$.
• The fixed fee is $3, so it should be the constant term added at the end (not multiplied by $d$).

Using the values from the problem:

• Rate per mile: $1.50 becomes $1.50d$.
• Fixed fee: $3 is added.

So the linear equation is $P = 1.50d + 3$, which matches choice B.