Slope comparison in two-phase regression analysis


I am using a two-phase regression analysis to analyze some physiological data. The analysis is based on using two, simple linear regressions (y=mx+b) where below x, the data is best described by Equation 1 and above x, the data is best described by Equation 2. The two equations are fit to the data to minimize RSS.

When plotted on a graph, the two regressions intercept at x,y and show an obvious 'breakpoint'.

My question is: How do I compare the slopes before and after the breakpoint?

I have used an f-test to compare the simple linear regression to the more complex two-phase regression to see if the two-phase regression describes the data significantly better. However, now I want to test to see if the slope of the equation fit to the data below x is significantly different than the slope of the equation fit above x (x being the intercept).

Note: This is a data series where individuals were warmed and changes in a physiological parameter measured. I have both individual data and mean data for n=12 individuals. Ideally, I would like to compare the slopes for each individual, and for the mean values.