Question

the credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). the remaining credit after 38 minutes of calls is $18.92, and the remaining credit after 74 minutes of calls is $13.16. what is the remaining credit after 87 minutes of calls?

Explanation:

Step1: Find the slope (rate of change)

The two points are \((38, 18.92)\) and \((74, 13.16)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{13.16 - 18.92}{74 - 38}=\frac{-5.76}{36}=-0.16\).

Step2: Use point - slope form to find the equation

Using the point \((38, 18.92)\) and \(m = - 0.16\), the point - slope form is \(y - y_1=m(x - x_1)\). So \(y-18.92=-0.16(x - 38)\). Simplify it to \(y=-0.16x+6.08 + 18.92=-0.16x + 25\).

Step3: Calculate the remaining credit at \(x = 87\)

Substitute \(x = 87\) into the equation \(y=-0.16x + 25\). Then \(y=-0.16\times87+25=-13.92 + 25 = 11.08\).

Answer:

\(11.08\)