#### Answer

See the explanation below.

#### Work Step by Step

(a)
Consider the provided statement: A car rental agency charges $\$200$ per week plus $\$0.15$ per mile to rent a car
Thus, to express the weekly cost to rent the car, the linear function representing the weekly cost of renting a car will be of the form $f\left( x \right)=mx+b$.
Suppose that traveling x miles will cost an equal amount in total for renting car from the agency per week.
Therefore, the agency that charges $\$200$ per week plus $\$0.15$ per mile fee will cost after traveling x miles and a week: $200+\left( 0.15 \right)x$.
Thus, by above given conditions
$f\left( x \right)=200+\left( 0.15 \right)x$
Hence, to express the weekly cost to rent a car:
$f\left( x \right)=200+\left( 0.15 \right)x$.
(b)
Consider the provided statement βThe weekly cost to rent the car was $\$320$ and the car rental agency charges $\$200$ per week plus $\$0.15$ per mile to rent a car.β
Thus, to calculate the number of miles driven during the week use the linear function representing the weekly cost of renting a car of the form $f\left( x \right)=200+\left( 0.15 \right)x$ from part (a).
The weekly cost to rent the car was $\$320$.
Therefore, from the above given condition.
$\begin{align}
& f\left( x \right)=200+\left( 0.15 \right)x \\
& 320=200+0.15x \\
& 120=0.15x \\
& \frac{120}{0.15}=x
\end{align}$
Further simplify,
$\begin{align}
& x=\frac{120}{0.15} \\
& =800
\end{align}$
Hence, the miles driven during the week were: $800\text{ miles}$.