Well, but consider (b/a) for a moment. The variance of (b/a) is:

var(b/a)

however, a = ybar - b*xbar so

var(b/a) = var(b / (ybar - b*xbar))

Which will not be very fun to try and solve. However, it can be approximated using the delta method, which is common when the exact SE is difficult.

var(a/b) can be found also in a similar manner.

~Matt