LDA project data line

I would like to project and plot vector line determined by eigenvalue problem (v) - in linear discriminant analysis. The first tutorial I saw, he didn't go through finding the eigenvalue or vector (Unless, I misunderstood). His solution was basically finding the mean of each class and the scatter of each one, to have the projected line. The second documentation did found the eigenvalue and vector to have the vector line project. I'm confused about so many materials. Could any one help me plot the project line and the projected data of each class with short explanation? Notice that my data is from tutorial, so it is not my real data, am just trying to understand for now, and then later I will do my own one.