Linear System Flyer

Sanzir

Martial Arts Fees

An example of a linear system is my karate classes. My siblings and I attend karate classes every week and the monthly payment can be put into a linear system.

Fees

The entrance fee for a single person is $5 and a monthly payment of $15. I can put this amount into a linear system or a linear equation;

Equation for single person graph

x axis is #of months
y axis is payment in $

y=mx+b
I am finding y which is the payment in x months.
m= dollars payment per month

x = #of months
b is y intercept or entrance fee of $5

Slope= rise

run

slope= 15

1

slope intercept form y=15x+5
or
standard form 15x-y+5=0


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Graph for myself and 2 siblings

I have two other siblings that take karate with me. The linear equation for the payment for all three of us can be put into a graph.

Equation for myself and two siblings

x axis is # of months

y axis is payment is $

y=mx+b

I am finding for y which is the payment in x months.
x is number of months
b is the y intercept or $30.

m is slope

slope=rise
run

slope=10

Therefore;
y intercept form y=10x+30
or
standard form 10x-y+30=0

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Comparing

Here is a graph that shows karate payment for me v.s me and my siblings.
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Summary

As shown on the graph, the point of intersection is (5,80). The point of intersection represents when the fees of the martial arts class will be the same; It will be $80 after 5 month for both graphs, or fees. After 5 months the fees for me and my siblings combined will be greater than the fee for only myself. Before 5 months the fees for only myself will be greater than the fees for me and my siblings.