# Linear System Flyer

### End-of-Unit Project

## The Different Variables

## Theater Prices - Per Movie Watched

## Equation

y = cost in dollars

m = $5

x = # of movies watched

b = upfront cost

**Theater One:**

b = $60

cost in $ = $5(# of movies watched) + upfront cost

cost in $ = $5(# of movies watched) + $60

y = 5x + 60

**Theater Two:**

b = $0

cost in $ = $15(# of movies watched) + upfront cost

cost in $ = $15(# of movies watched) + $0

cost in $ = $15(# of movies watched)

y = 15x

## Graphic Solution

**Theater One:**

y = mx + b

y = 5x + 60

90 = 5(6) + 60

90 = 30 + 60

90 = 90

**Theater Two:**

y = mx + b

y = 15x + 0

y = 15x

90 = 15(6)

90 = 90

Link to Desmo Graph:

## Why is this Important?

Even though this data is just a realistic simulation, its significance still closely applies to real life situations, in this case pertaining to money. Using this graph and this data we are able to see which option is cheaper for us depending on how many movies we might watch in that year. If we were to watch over six movies that year theater one would save us more money whereas if we were to watch less than six movies that year theater two would save us more money. The point at which the two lines intersect (6, 90) either option would cost the same amount of money. Data like this can help us make informed choices in the real world with almost anything, not just movie theater prices.

## Concluding Statement

Both of these plans will cost the same amount ($90) of money at six movies watched. Theater one will cost less for anything under six movies where theater two will cost less for anything over six movies.