Determining if reaction is endothermic or exothermic using equilbrium constant
Think about it this way.  In an exothermic reaction that is at equilibrium the forward reaction has a lower activation energy.  So, if you increase T the forward reaction rate increases but the reverse rate increases even more.  That's because the rates of reactions with higher activation energy are more sensitive to temperature.  With the reverse rate higher more reactants will be made until the concentration reactants reaches a point where the rate of the forward reaction equals the reverse rate.  

In an endothermic reaction increasing T increases the forward rate more than the reverse, producing more product until the increased product concentration causes the reverse rate to equal the forward rate.

The equilibrium constant can be thought of as a ratio of products to reactants needed to equalize the rates of two reactions with different activation energies.