for a given object does the doppler shift affect all wavelengths the same amount?

Let's say a particular spectrograph line is shifted 1,000 angstroms, from an original position of 4,000 angstroms. Does that imply that a line at 6,500 angstroms is shifted by 1,000 angstroms, as well? I read that visible light is affected more than radio wavelengths, and I want to clear it up. I always thought the doppler shift "moved" all wavelengths the same amount (as implied), but I saw a formula in another source that indicated the RATIO of the amount of shift versus the original wavelength was the same across the spectrum. I just want to clear it up.