Linear System Flyer

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

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

Comparing

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

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.