Final answer:
The correct equation for a 45% discount on movie tickets is y = 0.55x. This line is in the first quadrant because both the original price and the discounted price must be positive values.
Step-by-step explanation:
The student asked to write an equation representing the situation in which y is the price of the ticket with a coupon, and x is the original price of the ticket. Given a coupon for 45% off the price of a ticket, the equation that represents this situation is A) y = 0.55x. This equation indicates that the price of the ticket with the coupon is 55% of the original price, since 100% - 45% = 55%.
The line representing this equation should only be in the first quadrant because the values for the price of the ticket with the coupon (y) and the original price of the ticket (x) cannot be negative, as this would not make sense in real-world terms. In the context of a graph, the first quadrant is where both x and y have positive values, fitting the scenario of ticket pricing.