A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the amount of money it spends on advertising. If it spends $$10,000$ on advertising, then $100,000$ boxes of cereal will be sold, and if it spends $$90,000$ on advertising, then $200,000$ boxes of cereal will be sold.

$($a$)$ Write an equation that relates the amount A spent on advertising to the number $x$ of boxes the company aims to sell.

$($b$)$ How much advertising is needed to sell $300,000$ boxes of cereal?

$($c$)$ Interpret the slope.