Question

Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 100 minutes and the cost was $54.00. In July she used 660 minutes and the cost was $138.00.

Answer 1

The costs of the plan are $0.15 per minute and a monthly fee of $39

Explanation:

Let

x ----> the number of minutes used

y ----> is the total cost

step 1

Find the slope of the linear equation

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

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

we have the ordered pairs

(100,54) and (660, 138)

substitute

`m=(138-54)/(660-100)`

`m=(84)/(560)=\$0.15\ per\ minute`

step 2

Find the equation of the line in point slope form

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

we have

`m=0.15\\point\ (100,54)`

substitute

`y-54=0.15(x-100)`

step 3

Convert to slope intercept form

Isolate the variable y

`y-54=0.15x-15\\y=0.15x-15+54\\y=0.15x+39`

therefore

The costs of the plan are $0.15 per minute and a monthly fee of $39