I am trying to understand concave functions, for which wikipedia gives an expression written as:

now I am confused as how to understand this as the line over there says that this definition merely states that for every z between x and y, the point (z, f(z) ) on the graph of f is above the straight line joining the points (x, f(x) ) and (y, f(y) ). Now what I know is that the line joining two point should be $f'(u)= \frac{f(y)-f(x)}{y-x}u+c $ where f'(.) I have taken as straight line co ordinate. Now how does this equation fits the definition that f(z) should be above than f'(u)?