linear regression with multiple segments

I've searched for this issue but i cannot find it exactly. I have a set of data with that consists of several curves that I can linearize. The family of curves should have one variable the same and the other variable will be different for each curve(line). I want to find the best fit for this collection of lines for all the data en masse. I don't have the Statistical Package, but I feel this should be possible. The x values are usually the same for each line but not guaranteed. I'm not clear how to formulate the problem.