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 30 minutes of calls is $16.10, and the remaining credit after 59 minutes of calls is $12.33. What is the remaining credit after 77 minutes of calls?

Answer 1

The first thing we need to do is to find the slope of this linear function.

To find this slope, we do the following:

$m=\frac{16.10-12.33}{30-59}=-0.13$

Now, we should find the equation of this line and then replace by x=77 minutes:

$\begin{gathered} y=16.10-0.13(x-30) \\ y=-0.13x+20 \end{gathered}$

Replacing by x = 77:

$\begin{gathered} y(77)=-0.13(77)+20 \\ y(77)=9.99 \end{gathered}$

The remaining credit after 77 minutes of calls is $9.99.