SOLUTION: Omg, hopefully this is the last one. I do not understand this. Please somebody explain it to me and show me how to do these types of word problems. I greatly appre

Algebra ->  Graphs -> SOLUTION: Omg, hopefully this is the last one. I do not understand this. Please somebody explain it to me and show me how to do these types of word problems. I greatly appre      Log On


   

Question 174272:

Omg, hopefully this is the last one. I do not understand this. Please somebody explain it to me and show me how to do these types of word problems. I greatly appreciate it in advance.
Say there's a credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.12 . :(
There is a $23.00 credit remaining on the card after 25 minutes of calling. How much credit will there be after 33 minutes of calls?






Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of minutes and y=amount of credit remaining


In order to answer this question, we need to find the equation that models (ie represents) this problem.


Because "There is a $23.00 credit remaining on the card after 25 minutes of calling", this tells us that x=25 and y=23 which gives the point (25,23). So the line goes through this point.


Also, since the "function gives a line with a slope of -0.12", this tells us that our line has a slope of -0.12. So this means that m=-0.12


Note: "a slope of -0.12" tells us that for every minute that we talk, we lose $0.12 (or 12 cents).



If you want to find the equation of line with a given a slope of -0.12 which goes through the point (25,23), simply use the point-slope formula to find the equation:


---Point-Slope Formula---


y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point


So lets use the Point-Slope Formula to find the equation of the line


y-23=-0.12%28x-25%29 Plug in m=-0.12, x%5B1%5D=25, and y%5B1%5D=23 (these values are given)


y-23=-0.12x%2B%28-0.12%29%28-25%29 Distribute -0.12


y-23=-0.12x%2B3 Multiply -0.12 and -25 to get 3


y=-0.12x%2B3%2B23 Add 23 to both sides to isolate y


y=-0.12x%2B26 Combine like terms


So the equation of the line with a slope of -0.12 which goes through the point (25,23) is y=-0.12x%2B26


So this means that the equation tying together the amount remaining "y" and the number of minutes "x" is y=-0.12x%2B26



How much credit will there be after 33 minutes of calls?




To answer this question, we'll use the equation we just found.


y=-0.12x%2B26 Start with the given equation


y=-0.12%2833%29%2B26 Plug in x=33


y=-3.96%2B26 Multiply


y=22.04 Add


So after 33 minutes of calls, there will be $22.04 of credit left.