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 34minutes of calls is $25.92, and the remaining credit after 53 minutes of calls is $23.64. What is the remaining credit after 71 minutes of calls?

Answer 1

The remaining credit after 71 minutes is $21.48

To solve this, we can calculate the equation of the linear function that represents the remaining credit

x is the time in minutes, y is the remaining credit. the we have two points of the line and we can calculate the equation

34 min and $25.92 => (34,25.92)

53 min and 23.64 => (53,23.64)

the formula to calculate the slope of a line is

$m=\frac{y_2-y_1}{x_2-x_1_{}}=\frac{23.64-25.92}{53-34}=-0.12$

now we know the slope, we can get the line euqation

$y=m(x-x_1)+y_1\Rightarrow\text{ y=-0.12(x-34)+25.92=-0.12x+30}$

Now for wathever x we ask, just plug it in to the equation and will give you the reamining credit.

for x=71 min:

$y=-0.12(71)+30=-8.52+30=21.48$

theremaining credit is $21.48.