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 52 minutes of calls is 12.06 and the monthly cost for 100 minutes is 17.34. What is the monthly cost for 74 minutes of calls?

Answer: the monthly cost for 74 minutes of calls is 14.48

Step-by-step explanation:

let x represent the number of minutes for the month.

Let y represent the monthly cost for x minutes.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (17.34 - 12.06) / (100 - 52)

m = 5.28/48 = 0.11

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 52, y = 12.06 and m = 0.11 into y = mx + c. It becomes

12.06 = 0.11 * 52 + c = 5.72 + c

c = 12.06 - 5.72

c = 6.34

The linear function becomes

y = 0.11x + 6.34

The monthly cost for 74 minutes of calls would be

y = 0.11 * 74 + 6.34

y = 14.48