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 50 minutes of calls is $13.98 and the monthly cost for 78 minutes is $17.06 . What is the monthly cost for 77 minutes of calls?

Answer 1

To find the monthly cost for 77 minutes of calls on a linear long-distance phone plan based on given data at 50 and 78 minutes, we first calculate the slope of the line representing cost per minute, then apply it in the line equation to get the cost for 77 minutes, which is $16.95.

Step-by-step explanation:

The problem at hand is a linear function problem where we are to determine the cost of a long-distance phone plan based on minutes used. Given two points, (50, 13.98) and (78, 17.06), which signify minutes and cost respectively, we can find the linear equation that represents this relationship:

Let the cost be C and the minutes be m. First, we calculate the slope (m) of the line:

m = (17.06 - 13.98) / (78 - 50) = 3.08 / 28 = 0.11

This gives us the cost per additional minute of call time. Using the point-slope formula, we plug in one of the points and the slope to get the equation of the line:

C - 13.98 = 0.11(m - 50)

To find the cost for 77 minutes, we substitute m with 77:

C - 13.98 = 0.11(77 - 50)

C = 0.11(27) + 13.98 = 2.97 + 13.98 = $16.95

Therefore, the monthly cost for 77 minutes of calls would be $16.95.