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 31 minutes of calls is $18.25 and the monthly cost for 44 minutes is $19.42. What is the monthly cost for 33 minutes of calls?

The cost is;

$18.43

Step-by-step explanation:

The general model for a linear equation is;

y = mx + b

let y be the monthly cost in dollars

x is the number of minutes

b will represent the base cost

m is the cost of the call per minute

so let us get m and b

Thus, we have;

18.25 = 31m + b

19.42 = 44m + b

Subtract i from ii

(19.42-18.25) = (44-31)m

1.17 = 13m

m = 1.17/13 = 0.09

To get b, we substitute the value of m in any of the equation

18.25 = 31 m + b

18.25 = 31(0.09) + b

b = 18.25 - 2.79

b = 15.46

so, the equation of the line is;

y = 0.09x + 15.46

Now to get the cost for 33 minutes

simply substitute the value of 33 for x

we have this as;

y = 0.09(33) + 15.46

y = $18.43

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