# Phone Plans in 2014

### 2 of the best companies battle it out to give the best plans

## Here they are!!!

From Eno you must pay an upfront free of $50 also one time, and you will have to pay $8 per month.

To simplify this for you we have done some math so here it is.__Lebbs Plan__

__Equation__

First you must understand the variables.

y= total cost of plan

m= cost per month

x= the number of months

b= the starting price of the plan

__Formula__

*Slope and y intercept form:*

y=mx+b

y=5x+60

*Standard form:*

*Ax + Bx + C = 0*

*-5x + y - 60 = 0*

If you look below you will be able to see how your bill will add up progressively throughout the year.

**Enos Plan**

__Variables__

First you must understand the variables.

y= total cost of plan

m= cost per month

x= the number of months

b= the starting price of the plan

__Equation__

*Slope and y intercept form:*

y=mx+b

y=8x+50

*Standard form:*

*Ax + Bx + C = 0*

*-8x + y - 50 = 0*

If you look below you will be able to see how your bill will add up progressively throughout the year.

## So basically.....

If you are going to use this plan for 3 months or less, Eno would be a cheaper service provider for you.

If you are going to use this plan for over 5 months, Lebb would be a cheaper choice for you.

If you are going to use this plan for 4 months either plan will work as they are the exact same price.

## Questions

*In what month will the price of these two plans be exactly the same?*

To find what month the price of these two plans will be exactly the same, we must solve the linear equation/system, the result will be the point of intersection which is the answer to this questions.

The point of intersection can be found in two ways.

*Graphing*

Using the equations for each line, we can find the point of intersection by using the y intercept and rise over run for slope.

Lleb's plan

y=5x+60

- (0,60) is the y intercept, now plot it on the graph

- Then use rise over run to graph the slope which is 5

- Graph the line

Eno's plan

y=8x+50

- Repeat same steps

Then, using the 2 graphed lines, find the point of intersection. On the graph, the point of intersection is on the 4th month of usage.

Therefore the point of intersection is (4, 80) as shown in the diagram below.

## Why use a linear system?

A linear system tracks changes in rates at which something increases or decreases at. In this case linear systems are used to see which plan is better to suit a situation. This can help consumers decide on getting a better plan depending on their situation.