#### Answer

Discontinuous along the line $y=x$

#### Work Step by Step

Consider the function $f(x,y)=e^{1/x-y}$
Use maple command to plot the graph of the function as depicted below:
Suppose $x-y=0$
$y=x$
Therefore, the function $f(x,y)=e^{1/x-y}$is discontinuous at all points which satisfy $y=x$
Hence, the function is discontinuous along the line $y=x$