Question

The monthly cost in dollars of a long distance phone plan is a linear function of the total calling time in minutes. The monthly cost for 42 minutes of calls is $18.15 and the monthly cost for 90 minutes is $22.47. What is the monthly cost for 45 minutes of calls

Answer 1

The monthly cost for 45 minutes is $18.42

Explanation:

Let

x -----> the total calling time in minutes

y ----> the monthly cost in dollars

we have the ordered pairs

(42,18.15) and (90,22.47)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(22.47-18.15)/(90-42)`

`m=(4.32)/(48)`

`m=\$0.09\ per\ minute`

step 2

Find the linear equation in point slope form

`y-y1=m(x-x1)`

we have

`m=0.09\\(x1,y1)=(42,18.15)`

substitute

`y-18.15=0.09(x-42)`

step 3

Find the monthly cost for 45 minutes of calls

For x=45 min

substitute the value of x in the linear equation and solve for y

`y-18.15=0.09(45-42)`

`y-18.15=0.09(3)`

`y-18.15=0.27`

`y=0.27+18.15`

`y=18.42`

therefore

The monthly cost for 45 minutes is $18.42