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 47 minutes of calls is $18.90 and the monthly cost for 83 minutes is $23.22. What is the monthly cost for 64 minutes of calls?

Answer 1

The monthly cost for 64 minutes of calls would be $20.94

Explanation:

We need to create a linear function that represents the Monthly cost (vertical-axis) versus the number of minutes used (horizontal axis)

For such, we use the information they give us, which in fact represent two points on the plane of the form: (minutes, cost).

These points are:

(47, 18.90) representing the $18.90 monthly cost for 47 minutes used, and

(83, 23.22) for the second piece of information on 83 minutes for a monthly cost of $23.22.

We use the points to find the slope of the segment that joins the two points based on the formula for slope between points
`(x_1,y_1) \, and\, (x_2, y_2)`:

`slope = (y_2-y_1)/(x_2-x_1)`

For this case, our slope would be:
`slope = (23.22-18.90)/(83-47) =(4.32)/(36) = 0.12`

Since we know the slope of the line, now we use the point-slope form of a line to get the line's equation. We use the coordinates of one of the given points, for example (83, 23.22):

`(y-y_0)=m(x-x_0)\\(y-23.22)=0.12(x-83)\\y-23.22=0.12x-9.96\\y=0.12x-9.96+23.22\\y=0.12x+13.26`

Where x represents the number of minutes used, and y represents the monthly cost.

Now that we have the line that describes the cost, we can estimate the cost for 64 minutes of calls used by simply evaluating this linear function for x = 64:

`y=0.12x+13.26\\y=0.12*(64)+13.26\\y=7.68+13.26\\y=20.94`

Therefore, the monthly cost would be: $20.94