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 41 minutes of call is $14.17 and the monthly cost for 95 minutes is $19.03. What is the monthly cost for 61 minutes in calls?

$ 15.97

Step-by-step explanation:

Being a linear function, we can calculate the equation that determines this function in the following way:

y = m * x + b

let m be the slope and b the independent term or intercept.

We have two points: (41, 14.17); (95, 19.03)

Now the slope is equal to:

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

replacing

m = (19.03 - 14.17) / (95 -41)

m = 0.09

now the intercept can be calculated like this:

y = m * x + b; solve for "b":

b = y - m * x

replacing with the data of the first point (41, 14.17)

b = 14.17 - 0.09 * 41

b = 10.48

Therefore the function is as follows:

cost = 0.09 * (minutes) + 10.48

We are told that how much is the cost in 61 minutes in call, we only replace:

cost = 0.09 * (95) + 10.48

cost = 15.97

Which means that in 61 minutes of calling the monthly cost is $ 15.97