You seem to have reworded to "All eigenvectors that correspond to one a unique eigenvalue lie on the same line, but have different magnitudes." This is technica

You seem to have reworded to "All eigenvectors that correspond to one a unique eigenvalue lie on the same line, but have different magnitudes." This is technically true if you interpret "unique" to mean "multiplicity of one", but still seems confusing, especially as you have not yet discussed the multiplicity of eigenvalues. I would consider rephrasing the article as you do in the above comment, "when you find an eigenvector for one eigenvalue, then you can construct infinite number of eigenvectors by scaling that one".