# What is the error in the ratio of linear regression fit parameters?

I am fitting $y$ vs. $x$ data with a simple linear model:

$y = m x +b$

The quantity I am ultimately interested in is:

$R= \frac{m}{b}$

How can I calculate the standard error in the estimate of $R$ given the estimates of $m$ and $b$ along with the covariance matrix (which is not diagonal) obtained from an ordinary least-squares regression? The accepted answer will be instructive and not just a reference to the Wikipedia article on variance (it's not clear to me how to utilize the product of correlated variables equation given there).