Question

challenge a movie theater sends out a coupon for 30% 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.
the equation is y = □.
(use integers or decimals for any numbers in the expression).

Explanation:

Step1: Calculate discounted percentage

A 30% discount means the customer pays 70% of the original price, so $100\% - 30\% = 70\% = 0.7$.

Step2: Relate y and x

The discounted price $y$ equals 0.7 times the original price $x$.
$y = 0.7x$

Step3: Explain quadrant restriction

Ticket prices cannot be negative, so $x \geq 0$ and $y \geq 0$, which corresponds to the first quadrant (where both coordinates are non-negative).

Answer:

The equation is $y = 0.7x$.
The line only appears in the first quadrant because the original ticket price $x$ and discounted ticket price $y$ cannot be negative values.