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
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.