The exchange current is the current at equilibrium, i.e. the rate at which oxidized and reduced species transfer electrons with the electrode.  In other words, the exchange current density is the rate of reaction at the reversible potential (when the overpotential is zero by definition).  At the reversible potential, the reaction is in equilibrium meaning that the forward and reverse reactions progress at the same rates. This rate is the exchange current density.
The Tafel slope is measured experimentally.  It can, however, be shown theoretically that when the dominant reaction mechanism involves the transfer of a single electron that
where A is defined as 
where
*  is Boltzmann's constant,
*  is the absolute temperature, 
*  is the electric elementary charge of an electron,
*  is the thermal voltage, and 
*  is the "charge transfer coefficient", the value of which must be between 0 and 1.