Shakespear's Pizza sells $1,200$ large Vegi Pizzas per week for $$18$ a pizza. When the owner offers a $$5$ discount, the weekly sales increase to $1,700.$

$($a$)$Assume a linear relation between the weekly sales $A(x)$ and the discount x $.$ Find $A(x).$

$($b$)$Find the value of x that maximizes the weekly revenue.

$($c$)$Answer parts $($a$)$ and $($b$)$ if the price of one pizza is $$9$ and all other data are unchanged.

$($a$)A(x)=$