The credit remaining on a phone card In dollars Is a linear

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 23 minutes of calls Is $21.55, and the remaining credit after 49 minutes of calls Is $17.65. What Is the remaining credit after 63 minutes of calls?

Solution

As seen from the graph the remaining inutes a linear trend and it can be modelled by a inear equation if two points are given:

General form of Linear equation : y = mx +c

where m is slope and c is the y intercept

We are given two points : ( 23 min, $21.55 ) and ( 49 min ,$17.65)

slope m = ( 17.65 - 21.55)/( 49 -23) = -3.9/26 = -0.15 $/min

now find c using one of the two points:

y = -0.15x +c ----> 21.55 = -0.15*23 +c -----> c = 25

So, y= -0.15x +25

Now find how much credt after 63 min.Plug x= 63 and y

y = -0.15*63 +25 = $ 15.55