Answer
a) With the legislation allowing banks to pay interest on checking accounts, this increases the return to money (compared to other assets). In turn, this increases the demand for money.
Work Step by Step
b) Please see the graph. If the money supply remains at $MS_1$, the interest rate would increase from $r_1$ to $r_2$. However, this increased interest rate would decrease the levels of consumption and investment (aggregate demand).
c) For the interest rate to stay constant, the money supply would have to increase from $MS_1$ to $MS_2$ (as shown on the graph). The money supply could increase if the Fed decided to buy bonds on the market.