The IS curve shows those combinations of income and the interest rate for which aggregate expenditure equals income (or output). Its name derives from the fact that in an economy with no government (then T-G = 0) and no trade with other countries (then IM-EX = 0) the required balance of leakages out of and injections into the income circle [(S-I) + (T-G) + (IM-EX) = 0] obtains if I = S.

In an interest rate/income diagram the IS curve slopes downward. To show why we may proceed from a Keynesian cross diagram with the numbers plugged in that we used when discussing aggregate demand (see figure on the right):

First, suppose that the 400 units of investment occurred at an interest rate of 5%, due to an investment function that reads I = 600 - 40i. We may note this fact that at an interest rate of 5% equilibrium income is Y₁ by means of the red dot in the i/Y diagram below the Keynesian cross.

Next suppose that the interest rate drops to 2%. According to our investment function this raises investment to I = 600 - 40×2 = 520. This shifts the aggregate demand line up and raises equilibrium income to Y₂. So at the lower interest rate of 2% equilibrium income is higher. We may note this by means of another red dot, as shown in the second figure.

We might repeat this exercise numerous times and mark all interest rate/income combinations that clear the goods market by red dots in our i/Y diagram. All these dots would lie on the red line that runs through the two dots we identified so far. This red line is called the IS curve. It slopes downward to the right, indicating that higher equilibrium levels of income obtain at lower interest rates.

The IS curve is drawn with the understanding that other demand categories (that is G and NX) remain unchanged. If they do change, this amounts to shifting the IS curve.