How to determine if a 2-variable function $f(x, y)$ is convex when knowing what do to with 1 variable function $f(x)$?

Question

for example, $f(x,y) = -e^x log(y)$ for $x, y > 0$?

I fully understand how to determine whether a 1-variable function is convex, i.e. $f$ is convex on $[a, b]$ if $f(\alpha x + (1 - \alpha)y) \leq \alpha f(x) + (1-\alpha)f(y) $, $\forall \alpha \in [0,1] and x, y \in [a, b]$.