Use the two pieces of information as points $(d, C)$ on a line: one for the 6-mile trip and one for the 14-mile trip. How can you use these points to find the slope (cost per mile)?

Once you know the cost per mile (the slope), plug it and one of the points into $C = md + b$. What does solving for $b$ give you in this context?

In the equation $C = md + b$, what real-world quantity does $b$ represent for this delivery service?

In Desmos, create a table. In the first row, enter $(6, 13)$, and in the second row, enter $(14, 25)$ as your two $(d, C)$ points.

Under the table, type y1 ~ m x1 + b. Desmos will perform a linear regression through those two points and display values for m and b.

Look at the value of b that Desmos shows. That b is the fixed fee (the cost when the distance is 0 miles). Read off that value from the screen.

We are told the cost $C$ is a linear function of distance $d$, so we can write an equation of the form

Here:

• $m$ is the cost per mile (the slope).
• $b$ is the fixed fee (the starting cost when $d=0$), which is what the question asks for.

The information about the two trips gives us two points $(d, C)$ on the line:

• A 6-mile trip costs $13 $\Rightarrow$ $(6, 13)$
• A 14-mile trip costs $25 $\Rightarrow$ $(14, 25)$

We can use these two points to find the slope $m$ (the cost per mile) using the slope formula:

Now calculate the slope:

So the cost per mile is $1.5$ dollars. Now substitute $m = 1.5$ and one of the points into $C = md + b$ to find $b$.

Using the point $(6, 13)$:

From

first compute $1.5(6)$:

So

Subtract 9 from both sides:

The fixed fee the service charges is $\boxed{4}$ dollars.