Linear System Flyer

End-of-Unit Project

The Situation - Movie Theater Prices

At two different movie theaters there are two different payment options:


Theater 1

Pay $60 upfront and pay $5 for every movie you want to watch that year.


Theater 2

Pay $0 upfront and pay $15 every time you want to watch a movie that year.

The Different Variables

The variables in this situation are the "number of movies watched", "the cost in dollars" and "the upfront cost". The "number of movies watched" is the independent variable whereas "the cost in dollars" is the dependent variable. The cost in dollars depends on the number of movies watched. "The upfront cost" is a constant; it always stays the same.

Theater Prices - Per Movie Watched

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Equation

I will be expressing this situation in "y = mx + b" form:


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

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Graphic Solution

In the graph above we can see that the two lines intersect at point 90,6. To check this graphic solution we can use algebra to substitute x = 6 and y = 90 in our two equations we created above:


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:

https://www.desmos.com/calculator/kpwkknvgmh

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.