Answer to Question #135762 in Calculus for Promise Omiponle

Question #135762
For the function (2y+x)/(x-y-3)

write out an equation for a level curve for which f(x,y) = C. Your final equation should be of the form y = f(x,C). What is the level curve that goes through the point (1,2)?
1
Expert's answer
2020-09-29T18:09:02-0400

since function

"f(x,y)=c"


"c=\\frac{2y+x}{x-y-3}"


Since this curve passing through (1,2)

substitute x=1 and y=2

then,

"c=\\frac{4+1}{1-2-3}"


c="\\frac{-5}{4}"


so

"\\frac{-5}{4}=\\frac{2y+x}{x-y-3}"


-5x+5y+15=8y+4x


9x+3y=15

so

3x+y=5

y=5-3x

This is the required curve.


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