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.

Variables

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


=rise/run


=(5.50-5.00)/(1-0)


=0.5/1


=0.5


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:


y=0.5x+5


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


To change into Standard Form:


Ax+By+C=0


0.5x-y+5=0

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Cellular Plan #2

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Cellular Plan #2

To find the slope:


= rise/run


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


=1/1


=1


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:


y=x


To convert into Standard Form:


Ax+By+C=0


x-y=0

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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


So:


0.5x+5=x

5=x-0.5x

0.5x=5

x=10


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


y=0.5*10+5

y=5+5

y=10


To double check we subsitute x into the other equation:


y=10


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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Summary

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

Decision

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.