Question 165387
Since the "total cost increases by $3 for each additional unit made", this means that the slope is {{{m=3}}}. Also, because C(1,000) = 30,000 , this means that we have the point (1000,30000).



So let's find the equation of the line that has a slope of 3 and goes through the point (1000,30000)



If you want to find the equation of line with a given a slope of {{{3}}} which goes through the point (1000,30000), you can 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-30000=(3)(x-1000)}}} Plug in {{{m=3}}}, {{{x[1]=1000}}}, and {{{y[1]=30000}}} (these values are given)



{{{y-30000=3x+(3)(-1000)}}} Distribute {{{3}}}


{{{y-30000=3x-3000}}} Multiply {{{3}}} and {{{-1000}}} to get {{{-3000}}}


{{{y=3x-3000+30000}}} Add 30000 to  both sides to isolate y


{{{y=3x+27000}}} Combine like terms {{{-3000}}} and {{{30000}}} to get {{{27000}}} 

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Answer:



So the equation of the line with a slope of {{{3}}} which goes through the point (1000,30000) is:


{{{y=3x+27000}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=3}}} and the y-intercept is {{{b=27000}}}



So in function notation, the cost function is {{{C(x)=3x+27000}}}. So you are correct.