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 32 minutes of calls is $15.98 and the monthly cost for 88 minutes is $23.26. what is the monthly cost for 54 minutes of calls?

Explanation:

Step1: Find the slope of the linear function

We have two points \((x_1, y_1) = (32, 15.98)\) and \((x_2, y_2) = (88, 23.26)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{23.26 - 15.98}{88 - 32}=\frac{7.28}{56}=0.13\).

Step2: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\), substitute \(m = 0.13\), \(x_1 = 32\) and \(y_1 = 15.98\). So \(y-15.98 = 0.13(x - 32)\). Expand it: \(y-15.98=0.13x-4.16\), then \(y=0.13x - 4.16 + 15.98=0.13x+11.82\).

Step3: Calculate the cost for 54 minutes

Substitute \(x = 54\) into the equation \(y = 0.13x+11.82\). Then \(y=0.13\times54 + 11.82=7.02+11.82 = 18.84\).

Answer:

\(18.84\)