Challenge A movie theater sends out a coupon for 15% 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= 0,65 x

If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately  pays (y) is  the original price (x) minus a 35% of this price: y= x -0.35 x . By association: y= (1-0.35) x and then y= 0.65 x.

The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).

Step-by-step explanation:

The price without discount (or without the coupon) is x.

The price with discount (or with coupon) is y.

y and x are both related: y is a percentage of x, specifically, y is 35% smaller than x. This means that y =0.65 x.