An encryption scheme is said to achieve perfect secrecy if for every probability distribution over M (the messsage space), every message m$\in$M and every ciphertext c$\in$C for which Pr[C = c]>0:

Pr[M = m | C = c] = Pr[M = m] or, equivalently, Pr[E(K,m)=c]=Pr[E(K,m')=c] where E is the encryption algorithm that encrypt the message M according to the key K.

So I think you should define/identify also the probability distribution over the message space(M) before starting to talking about perfect secrecy. However, I think the AffineCipher cannot achieve perfect secrecy except in particular cases in which the probaiblity distributions are too much flat.

An encryption scheme is said to achieve perfect secrecy if for every probability distribution over M (the messsage space), every message m$\in$M and every ciphertext c$\in$C for which Pr[C = c]>0:

Pr[M = m | C = c] = Pr[M = m] or, equivalently, Pr[E(K,m)=c]=Pr[E(K,m')=c] where E is the encryption algorithm that encrypt the message M according to the key K.

So I think you should define/identify also the probability distribution over the message space(M) before starting to talking about perfect secrecy. However, I think the AffineCipher cannot achieve perfect secrecy except in particular cases in which the probaiblity distributions are too much flat and the message to be enciphered very short.