Imagine you are a city planner working on improving transportation routes in a bustling metropolis. Your task is solving several geometric and graphical challenges related to a proposed road project connecting linearly to different locations. Solving these challenges contributes to an efficient urban transportation network, benefiting residents and visitors alike.
i) Optimal Route Planning: Determine the equation of the road that seamlessly connects critical locations, Points A (5,7) and B (6,5)
ii) Traffic Flow Analysis: Calculate the road's slope between A and B for efficient traffic design.
iii) Enhanced Traffic Safety: Determine the changes in road elevation from A to B, focusing on safety and convenience.