Question

question a cellular service provider charged one customer $40 for 150 minutes of airtime and another customer $55 for 300 minutes. what linear model represents the total cost, c, as a function of t, the number of airtime minutes? provide your answer below: c(t)=□

Explanation:

Step1: Find the slope of the linear model

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 150\), \(y_1=40\), \(x_2 = 300\), \(y_2 = 55\).

$$m=\frac{55 - 40}{300 - 150}=\frac{15}{150}=\frac{1}{10}$$

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\) to find the equation

Substitute \(m=\frac{1}{10}\), \(x_1 = 150\), \(y_1 = 40\) into \(y - y_1=m(x - x_1)\).

$$C-40=\frac{1}{10}(t - 150)$$

$$C-40=\frac{1}{10}t-15$$

$$C=\frac{1}{10}t + 25$$

Answer:

\(C(t)=\frac{1}{10}t + 25\)