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

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) (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 and 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

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 which goes through the point (25,23), simply use the point-slope formula to find the equation:

---Point-Slope Formula---

where is the slope, and

is the given point

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

Plug in , , and (these values are given)

Distribute

Multiply and to get

Add 23 to both sides to isolate y

Combine like terms

So the equation of the line with a slope of which goes through the point (25,23) is

So this means that the equation tying together the amount remaining "y" and the number of minutes "x" is

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

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

Start with the given equation

Plug in

Multiply

Add

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