The slope of the LM curve depends on the interest rate elasticity and the income elasticity of the money demand function.

A proof:

The Classical Economists see price expectations adjusting rapidly, making the AS curve vertical.

Things that shift the IS and LM curves also shift the AD curve.

Increase M:

The effect depends on the slopes of the curves:

A Liquidity Trap arises if the LM Curve has a flat region.

From the Loanable Funds Market:

The LM curve:

Fiscal (top) and monetary (bottom) policy:

The Keynesian and Classical Models have distinctly different implications.

The Classical Model business cycles:

This Phillips Curve handout shows how the actual evidence compares to the implications of these two models.