# Which Plan should Smith buy?

### By: Romanch Shah

## The situation(cost/extra minute)

## The variables

**minutes(x)**and the dependent variable is

**cost(y).**The number of minutes Smith uses determines the cost.

y represents the number of minutes

x represents the cost

## The data (table of values)

## The equations in slope y-intercept form

y=mx+b

y=0.6*x+*30.75

rate of change:0.6x first difference(6/10)

constant:30.75

Cost for Telus(CAD):

y=mx+b

y=0.5*x+*35

rate of change:0.5 first difference (5/10)

constant:35

## The standard form

y=0.6*x*+30.75

100(0.6*x*-y+30.75)=100(0) Multiply by 100 to get rid of the decimals and

60*x-*100y*+*3075*=*0 subtracted y from both sides.

standard form: 60*x*-100y+3075=0 or 60*x*-100y=-3075

Telus:

y=0.5*x+*35

10(0.5*x*-y+35)=10(0) Subtracted y from both sides and multiplied by 10 to get rid of the

5*x*-10y+350 decimals.

standard form: 5*x*-10y+350=0 or 5*x*-10y=-350

## The graph

-Bell:Blue line

-Telus:Red line

P.O.I.:(42.5,56.25) At 42.5 minutes the cost for both companies is $56.25.

## Using equations to solve the P.O.I.

*x+*30.75=0.5

*x+*35

0.6*x*-0.5*x=*35-30.75 Rearranging to group like terms

0.1*x*=4.25 Isolating x

*x*=42.5

Plug x into any equation, because at this point both points have the same x and y value.

y=0.5*x+*35

y=0.5(42.5)+35

y=21.25+35

y=56.25

P.O.I.:(42.5,56.25)

## Significance of the linear system

## Conclusion

**Bell** is better when he uses **less** than** 192.5 minutes** per month (150 minutes+42.5 minutes), while **Telus** is better when he **goes over** than **192.5 minutes per month**.