When performing bayesian linear regression, one needs to assign a prior for the slope $a$ and intercept $b$. Since $b$ is a location parameter it makes sense to assign an uniform prior; however, it seems to me that $a$ is akin to a scale parameter and it seems unnatural to assign an uniform prior to it.
On the other hand, it doesn't quite seem right to assign the usual uninformative Jeffrey prior ($1/a$) for a slope of a linear regression. For one, it can be negative. But I fail to see what else it could be.
So what is the "proper" uninformative prior for the slope of a bayesian linear regression? (Any references would be appreciated.)