The IS-LM model has been a staple of mainstream, undergraduate macroeconomics for several decades.
The IS curve purports to plot all points of the rate of interest (i) and the level of income (y) which are brought about by equilibrium between saving and investment. Investment is inversely related to i and saving is directly related to y. At a larger y, saving will be larger and therefore equal to investment only at a lower i. The IS curve, therefore, slopes downward to the right when plotted on a graph with i on the vertical axis and y on the horizontal axis.
The LM curve purports to plot all points of equilibrium between i and y which are brought about by equilibrium between the money stock and money demand (so called, liquidity preference). Although the money stock is independent of either i or y, liquidity preference varies directly with each. With a given money stock, the increasing effect of a larger y on money demand would have to be offset by a decreasing effect of a higher i to maintain equilibrium. The graph of LM slopes upward to the right when superimposed on the IS graph.
The intersection between IS and LM illustrates the only combination of i and y that has the entire economy, both the “real” and “money” aspects, in equilibrium.
The fundamental problem with IS-LM is the erroneous theories underlying it. Time preference determines both the interest rate and the extent of saving-investing. Money demand relative to the stock of money determines the purchasing power of money. Furthermore, it has no theory of production, no capital theory.
Roger Garrison compares and contrasts the Austrian, Keynesian, and Monetarist approaches to macroeconomics in his book, Time and Money. Here is an overview by Garrison: