Question

Julie is comparing cell phone plans that charge by the month. Let x represent the number

of minutes over 200 minutes, and let y represent the total cost in dollars. Plan A is
represented by the equation y=0.2x+20. Plan B is represented in the graph.

Which plan charges more per minute over the 200 minutes that are included?​

Answer 1

Before consuming 100 minutes over the 200 minutes included plan B is cheaper, After consuming 100 minutes over the 200 minutes included plan A is cheaper.

Explanation:

We need to derive the equation for Plan B. For that we can take two points in the graph.

Point P (x=0, y=15)

Point Q (x=20, y=20)

Replacing this in the general formula of a straight line (y=mx+x, where x and y are coordinates, m is the slope and n is the intercept) we get two equations, from which we get m and n.

y=0.25*x+15

We need to know at which point both lines meet each other, where both y (total cost) are the same. We do that by equalising the equations.

We get that at 100 minutes both plans cost the same (noth have the same y). Then, it's a matter of knowing which plan costs more before and after those 100 minutes. By making a rough sketch of the equations (you may do one more precise yourself to see it more clearly) we see that before x= 100 min plan b has a lower cost (lower y), but after plan A is more attractive (has a lower y).