# Sketching level curves of a function for given values

For $$f(x,y)=\ln(x-y)$$, sketch the level curves for the values $$k=-1,0,1$$

If we set $$f(x,y)=k$$, then for the values $$k=-1,0,1:$$

$$y= \begin{cases} x-e^{-1}\\ x-1\\ x-e^{} \end{cases}$$

Graphing these gives:

• For me it is correct. – user376343 May 30 at 9:04

$$\ln(x-y)=k$$
$$x-y=e^{k}$$
$$y=x-e^{k}$$
Therefore, the level curves are straight lines with the slope of $$1$$ and $$y$$-intercept $$-e^k$$