Mathematics: 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

The monthly cost in dollars of a long distance

tobyhollingsworth178

09.01.2022

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

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