help me please

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
$15.20
, and the remaining credit after
58
minutes of calls is
$10.72
. What is the remaining credit after
66
minutes of calls?

Answer 1

The fact that remaining credit is a linear function of the minutes used means that we should be able to write a function that looks something like this (this will be more obvious if the variables x and y are used):

 

Point-Slope

 

y - y₁ = m (x - x₁₎

 

The given information is like two points on the graph of a straight line.

 

When x = 30, y = 15.20; when x = 58, y = 10.72.

 

That means that the slope of the line can be calculated by:

 

m = (10.72 - 15.20)/(58 - 30) = -.16. That means for every minute that is used, the credit remaining goes down by 16 cents.

 

Using point slope:

 

y - 15.20 = -.16 (x - 30)

 

or

 

y = -.16 (x - 30) + 15.20

 

We want to know what the value of y will be when x = 66. Just plug 66 in for x in the above equation and evaluate y.

 

I got: $9.45.