When astronomers observe the spectra of distant galaxies, they notice that the hydrogen emission lines are shifted noticeably toward the red end of the visual spectrum, a phenomenon called red shift. red is lowest frequency of visible light. what does red shift indicate about the movement of the distant galaxies?

The amount of redshift increases in relation with the distance, meaning, the larger the redshift, the more distant the galaxy.  The Hubble diagram which was created by Edwin Hubble in 1929 shows that the more redshifted a galaxy is the further away it is. The galaxies are moving away from Earth because the fabric of space itself is expanding.  Subtle changes in the color of starlight let astronomers find planets,  measure the speeds of galaxies, and track the expansion of the universe.