Question 174272
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[1]=m(x-x[1])}}} where {{{m}}} is the slope, and *[Tex \Large \left(x_{1},y_{1}\right)] is the given point



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



{{{y-23=-0.12(x-25)}}} Plug in {{{m=-0.12}}}, {{{x[1]=25}}}, and {{{y[1]=23}}} (these values are given)



{{{y-23=-0.12x+(-0.12)(-25)}}} Distribute {{{-0.12}}}



{{{y-23=-0.12x+3}}} Multiply {{{-0.12}}} and {{{-25}}} to get {{{3}}}



{{{y=-0.12x+3+23}}} Add 23 to both sides to isolate y



{{{y=-0.12x+26}}} 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+26}}}



So this means that the equation tying together the amount remaining "y" and the number of minutes "x" is {{{y=-0.12x+26}}}




<h4>How much credit will there be after 33 minutes of calls?</h4>



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



{{{y=-0.12x+26}}} Start with the given equation



{{{y=-0.12(33)+26}}} Plug in {{{x=33}}}



{{{y=-3.96+26}}} Multiply



{{{y=22.04}}} Add



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