91Ó°ÊÓ

given,

$f(x,y)=−\frac{2y}{x}$

$\frac{1}{2}$Then for $c=−3,−\frac{2y}{x}=−3\text{that is}2y−3x=0$

Which is the equation of a straight line passing through the origin with a slope $\frac{3}{2}$

For $c=−2,−\frac{2y}{x}=−2\text{that is}y−x=0$

Which is the equation of a straight line passing through the origin with slope 1

For $c=−1,−\frac{2y}{x}=−1\text{that is}2y−x=0$

Which is the equation of a straight line passing through the origin with a slope$\frac{1}{2}$

For $c=0,−\frac{2y}{x}=0thatisy=0$

Which is the x-axis

For $c=1,−\frac{2y}{x}=1\text{that is}2y+x=0$

Which is the equation of a straight line passing through the origin with a slope $\frac{-1}{2}$

For $c=2,−\frac{2y}{x}=2\text{that is}y+x=0$

Which is the equation of a straight line passing through the origin with slope $-1$

For $c=3,−\frac{2y}{x}=3\text{that is}2y+3x=0$

Which is the equation of a straight line passing through the origin with a slope$-\frac{3}{2}$