A movie theater sends out a coupon for 95​% off the price of a ticket. Write an equation for the​ situation, where y is the price of the ticket with the​ coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.

Answer:y = 0.05xStep-by-step explanation:A movie theater sends out a coupon for 95​% off the price of a ticket, so the price of the ticket with the​ coupon is 100% - 95% = 5% of the original price.Let x = original pricey = price of the ticket with the​ couponThen x - 100%y - 5%Write a proportion:[tex]\dfrac{x}{y}=\dfrac{100}{5}[/tex]Cross multiply:[tex]100y=5x\\ \\y=0.05x[/tex]Since the original price and final price are always greater than 0, then the graph of this equation is in the first quadrant (see attached diagram)