option B = 4 per month plus 2.50 for each movie.
the breakeven point is when cost for option A equals cost for option B.
that occurs when 13 = 4 + 2.5 * x
x is the number of movies watched.
subtract 4 from sides of the equation to get 9 = 2.5 * x
solve for x to get x = 9/2.5 = 3.6
at less than or equal to 3 movies, option A is more expensive.
at greater than or equal to 4 movies, option B is more expensive.
you have two equations.
they are:
y = 13 and y = 4 + 2.5 * x
subtract the second equation from the first to get:
y = 13 - 4 - 2.5 * x
simplify to get:
y = 9 - 2.5 * x
when the graph is positive, option A is more expensive.
when the graph is negative, option B is more expensive.
the graph looks like this.
you can also graph the equations separately.
you would graph y = 13 and y = 4 + 2.5 * x
that graph looks like this.
you can also create a table around the breakeven point.
the table would look like this:
x y1 = 13 y1 = 4 + 2.5 * x y1 - y2 2 13 9 4 3 13 11.5 1.5 4 13 14 -1 5 13 16.5 -3.5
all graphs and tables point to the fact that, at 3 movies or less per month, option A is more expensive, while at 4 movies or more per month, option B is more expensive.
ana would need to watch 4 movies or more per month to make option A worth the cost.