Question

If a change in the real interest rate has no effect on planned investment spending or net exports, what does this imply about the slope of the IS curve ?

Short answer

The IS curve is vertical & parallel to Y axis, having slope = 0

Step-by-step solution

Basic Concept 

IS curve denotes combination of interest rate & income, at which goods market is at equilibrium. It is usually a downward sloping curve showing inverse relationship between interest rate & income for output of goods equilibrium.

As increase in interest rate leads to decrease in investment expenditure & net exports, which subsequently decreases aggregate Demand & equilibrium output (& vice versa also)

Detail Explanation 

If interest rate doesn't effect investment expenditure & net exports, it doesn't effect aggregate demand & finally equilibrium output also.

So, in this case there is no relationship between interest rate & output level, & the former doesn't effect latter.

Hence, the curve is vertical & parallel to Y axis with 0 slope, showing constant output level at various interest rate levels.