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 39 minutes of calls is $25.32, and the remaining credit after 57 minutes of calls is $23.16. What is the remaining credit after 60 minutes of calls?

Answer 1

One way to write a linear equation is the formula y = mx + b where m is the slope of the function and b is the y-intercept. For this reason, it is known as slope-intercept form.

The slope os calculated via the formula $\frac{y_2 - y_1}{x_2 - x_1}$. Lets calculate the slope of the equation first.

$\frac{23.16 - 25.32}{57 -39}$

$\frac{-2.16}{18}$

$-0.12$

So the slope is -0.12. This means for every minute of time used, $0.12 of credit is used. Next, lets plug in the value for m, and the values of an x and y point to find b.

y = 0.12x + b

23.16 = -0.12(57) + b

23.16 = -6.84 + b

30 = b

So, our final equation is y = -0.12x + 30.

Finally, we can use this equation to find the answer to the last part by plugging the value into x.

y = -0.12(60) + 30

y = -7.2 + 30

y = 22.8

So when 60 minutes have been used, there will be $22.80 worth of credit left.