the exchange rate is flexible, the central bank has perfect control
over the money supply. It thus also controls the position of the
LM curve. The FE curve is tied down by the world interest rate (ignoring
depreciation expectations). So these two curves alone determine
income. The position of the IS curve depends, among others, on the
exchange rate, which is flexible, endogenous. Market forces always
drive the exchange rate so as to move the IS curve into the point
of intersection between LM and FE.
This has the advantage that if we analyse policy measures
or changes in the economic environment under flexible exchange rates,
we only need to trace what happens to the LM curve and the FE curve,
while resting assured that the IS curve follows suite.
As examples, you may view animated displays of the consequences
a money supply increase
an increase of the world interest rate.