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

Answer:

The monthly cost for 45 minutes is $18.42

Step-by-step 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

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{22.47-18.15}{90-42}$

$m=\frac{4.32}{48}$

$m=\ 0.09\ per\ minute$

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