Hi Paula;

*A phone company has two different long distance phone plans. Plan A charges a monthly fee of $8.51 plus $0.05 per minute. Plan B charges a monthly fee of $6.15 plus $0.08 per minute.*

*A) Find a function for each long distance plan treating number of minutes used as the independent variable and cost as the dependent variable*

Plan A...y=0.05x+8.51

x=quantity of minutes, independent variable

y=total cost, variable dependent upon x

Plan B...y=0.08x+6.15

*B) Graph each of the two functions on the same cartesian plane*

Unfortunately, I cannot do that here. However, I can explain how to do it.

Both equations are in slope-intercept format...

y=mx+b

m is the slope.

b is the y-intercept, value of y when x=0.

Plan A slope intercept, (0,8.51).

Plan B slope intercept, (0,6.15)

You may also want to establish the x-intercepts, value of x when y=0.

Plan A...y=0.05x+8.51

0=0.05x+8.51

-8.51=0.05x

-170.2=x

(-170.2,0)

Plan B...y=0.08x+6.15

0=0.08x+6.15

-6.15=0.08x

-76.875=x

(-76.875,0)

Plot all four points, and draw the appropriate lines.

*C) Find the number of minutes for which the cost of plan Z equals the cost of plan B. What is the cost of each plan at this number of minutes? Label this point on the graph*

Plan A=Plan B

0.05x+8.51=0.08x+6.15

8.51=0.03x+6.15

2.36=0.03x

78.67=x

Let's find the value of y corresponding to this...

Plan A...y=0.05x+8.51

y=[(0.05)(78.67)]+8.51

y=12.44

Let's check this result with the other equation...

Plan B...y=0.08x+6.15

y=[(0.08)(78.67)]+6.15

y=12.44

The lines will meet at (78.67,12.44).