Suppose you calculate implied volatilities from the quoted prices of a

whole range of European calls and puts on the same stock, with the

same maturity date, but the options have different strike prices. If the

Black$-$Scholes equation correctly prices these options what would you

expect to observe in a graph of implied volatility $($on the y$-$axis$)$ against

the different strike prices $($on the x$-$axis$)?$