How do you determine a confidence level for two measurements with standard deviations?

Let's say you have two sets of data and you've fit them to a line and you'd like to give the confidence that the slopes of the lines are the same. Most fitting algorithms will provide an error for the slope, either from residuals or covariance or what have you. Any 'confidence' table I find (t-test, f-test, chi2, etc) needs the number of measurements/degrees of freedom to get the p-value. In the scenario I gave, I can understand how one could get the number of degrees of freedom (# data - fitting parameters), but what is the appropriate N? Is it different if you have a small or large set of data that you're fitting? Alternatively, what if all you have are the results of the fit, say 721 +/- 22 vs. 737 +/- 24. Shouldn't you be able to give a confidence estimate that they are the same or different?