Q:

Determining if a function of two variables is convex

We are told that a function is convex only if the following inequality holds:
f(tx + (1 - t) x' , ty + (1 - t) y') ≤ tf(x, y) + (1-t) f(x', y')
for 0 ≤ t ≤ 1 and all pairs of points (x, y) and (x', y'). 
What does this mean geometrically?  

A:

Draw the graph of a convex function and pick two points on the graph.  The line interpolating these two points lies above the graph. 