Question

A movie theater sends out a coupon for 85​% 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).

Answer 1

`y=0.15x`

Explanation:

Given:

Original price of the ticket is
`x`

Price after using the coupon is
`y`

Coupon discount is 85% of
`x=0.85x`

Therefore, the price after applying coupon is given as the difference of the original price and the coupon discount. That is,

`y=x-0.85x=x(1-0.85)=0.15x\\\therefore y=0.15x`

The graph is shown below. The graph passes through the origin as the above relationship is a proportional relationship.

The line
`y=0.15x` strictly remains in the first quadrant as both
`x` and
`y` can't be negative as they represent price of tickets and price can never have negative values. Hence, only the first quadrant has both the values of
`x` and
`y` positive.