If you look just right of center in the photo above, you can see the canyon of Bright Angel Creek and the linear pattern that it follows. Erosion worked preferentially at removing the crushed and broken rocks along the fault line, giving the canyon its unusually straight appearance. The picture below provides a closer perspective.
Faulting has influenced the region numerous times in the history of the Kaibab Plateau, including episodes of faulting in Proterozoic time 1.7 billion years ago that were primarily compressional in nature. Later, another period of mainly extensional faulting took place around 600-800 million years ago as the ancient supercontinent of Rodinia was breaking up. As can be seen in the geologic map below of the Bright Angel Creek area, the ancient rocks are riddled with faults (the entire map of the eastern part of Grand Canyon National Park can be found at http://pubs.usgs.gov/imap/i-2688/i-2688.pdf).