6. A popular kid's game has 15 tiles and 1 open space. The goal of the game is to rearrange the tiles to put them in order (from least to greatest, starting at the upper left-hand corner and going across each row). Use the figure to write the transformation(s) that describe the path of where the 8 tile is currently, and where it must be by the end of the game. Can this same translation be used to describe the path of all the tiles?

the first phase of the government’s plan for settlement was building the transcontinental railroad. the railroad provided a way to bring settlers and manufactured goods west and ship their agricultural and mining produce east. the transcontinental railroad was an essential artery for rapid development of the frontier.

the second phase of the government’s plan was a liberal land distribution policy that made it possible for many people to homestead. with these two key elements—transportation and cheap land—the government rapidly achieved its goal of persuading people to move west, settle on farms, and push back the frontier.