Question

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)?

Answer 1

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.