Equation 3 is the investment function which says that the higher the rate of interest the more attractive are risk free government securities versus risky private investments. Thus the amount of private investment decreases as the interest rate increases. To invest in a private project, the rate of return must equal the market interest rate plus a premium for the higher risk.
Individuals hold a portfolio of assets such as money, stocks, bonds, real estate, etc.
The individual holds money in the portfolio to take advantage of opportunities which may present themselves. As the interest rate rises the opportunity cost of holding money increases and he or she shifts from money to other assets. Solution to the IS-LM model How to solve the IS model is in the notes. Remember IS slopes down to right while LM slopes up to right. D Y that was derived in the notes.