Linear System Flyer

By: Rutvik Patel

Buying Cellular Plan

My friend wants to buy a cellular plan from 2 promotional offers this Christmas. The first offer has a fixed (inital) cost of $5 and every minute of use costs him $0.50. The other offer has no fixed (initial) cost but costs $1 for every minute used.


Independent Variable - Number of Minutes

Dependent Variable - Total Cost (in $)

Which Offer is Better

To find which offer is better, we must convert the given data into slope intercept form/ standard form, or graph and see which plan is better for each situation.

Cellular Plan #1

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Cellular Plan #1

To find the slope





Therefore the slope is 0.5.

The y intercept is 5, as that is where the line touches the y-axis.

Therefore the equation for slope intercept form is:


where y is the total cost and x is the number of minutes.

To change into Standard Form:



Big image

Cellular Plan #2

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Cellular Plan #2

To find the slope:

= rise/run

= (1-0)/(1-0)



Therefore the slope is 1.

The y intercept is 0, as that is where the line intersects the y- axis.

Therefore the equation in Slope Intercept Form is:


To convert into Standard Form:



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Point of Intersection

To find the point of intersection, we must look at the 2 equations.

For plan #1: y=0.5x+5

For plan #2: y=x






Now we subsitute the value of x into the 1 of the equations:




To double check we subsitute x into the other equation:


Now that both of y's are the equal we know that the y point is correct.

Therefore, the point of intersection is (10,10).

We can also double check by looking at the graph.

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Both Cellular Plans will cost the same amount ($10) for 10 minutes of usage. This is also the point of intersection.


As we can see from the graph Cellular Plan #2 is cheaper if he doesn't exceed 10 minutes. If he likes to use more that 10 minutes than he should chose Cellular Plan #1.

Significance of Solution

The graph helps compare the costs of various plans in real life as well by chosing an appropriate plan it can save significant dollars for the users.