The economy begins in equilibrium at point E, representing the real interest rate r1 at which saving S1 equals desired investment I1. What will be the new equilibrium combination of real interest rate, saving, and investment if there is a tax law change that makes investment projects less profitable and decreases the demand for investment goods (but does not change the amount of taxes collected in the economy)

The economic graph that is referred to in the question in referred to as the IS-LM curve which depicts the intersection of the IS (Investment-savings curve) with the LM (liquidity preference-money supply) curve. This intersection determines thr equilibrium between real interest rates and the output/consumption at that level of interest rate. The IS curve is downward sloping while the LM curve is upward sloping.

The tax law change makes the investment less attractive which will cause the IS curve to pull inwards (i.e a shift to the left). This shift to the left essentially reduces the level of investment thereby lowering the demand for money for investment. This reduction in demand causes the real interest to decrease. At this decreased interest level, there is a decrease in the the level of savings (because of the lower return that is available on money saved). Therefore the impact will result in a new lower equilibrium at which the real interest rate and the levels of saving and investment will be lower than the original equilibrium level.