level curve

Level curves are like contour lines but for 3D functions.

To sketch level curves for a function, determine a range of $z=f(x,y)$ values and step size (e.g. from -2 to 2 with step size 1, meaning $c\in \left\{-2,-1,0,1,2\right\}$). Then for each value of $c$: set $c=f(x,y)$, solve for $y$, and draw the resulting curve.