If $f(x,y)$ is a function that its contour lines are straight, is it necessary looks like $f(x,y) = ax + by + c$

Question

If $f(x,y)$ is a function that its contour lines are straight, is it necessary looks like $f(x,y) = ax + by + c$?

Well, in the answer is no. it is written that $e^{x+y}$ for every $(x,y)$ has straight contour lines. I'm not sure they're correct, can you explain or give another example of a function which its contour lines are straight? or explain how to solve this question efficiently?

Thank you very much in advance.

Edit: In wolfram alpha, $e^{(x+y)}$ are straight lines, but how can I know that during an exam where I don't have any tools except a calculator?

Answer 1

Contour line is defined as $\{ (x,y) | f(x,y) = constant \}$. So for $e^{x+y}=C$, you get $x+y = \ln C$, which is a straight line. The answer is correct. Another strange example would be $(15x+6y)^{100}$.