# Linear System Flyer

## 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.

## 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

## 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