Linear System Flyer
By: Rutvik Patel
Buying Cellular Plan
Variables
Dependent Variable - Total Cost (in $)
Which Offer is Better
Cellular Plan #1
Cellular Plan #1
=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
Cellular Plan #2
Cellular Plan #2
= 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
Point of Intersection
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.