Scenic World's railway line is the steepest
The steepest railway line is in Scenic World, Blue Mountains, NSW, Australia at a whopping 52 degrees below horizontal.
The steepest incline plane in the world is the Nanjing Yangtze River Bridge in China, which features a railway line with a gradient of 38 degrees. However, the steepest railway incline is often cited as the Gelmerbahn in Switzerland, which has a maximum gradient of 106%. These inclines are used for different purposes, with the Gelmerbahn primarily serving tourists and the Nanjing Bridge facilitating transportation.
Your mother's line
Steepest line possible dealing with slope is up to, but not including infinity.
A vertical line.
potty
Pechenga, north of Murmansk, in Russia, has probably the world's northernmost public railway line.
London's Metropolitan line is the oldest underground railway in the world, dating from 1863
Takabisha is the world's steepest roller coaster located at Fuji-Q Highland in Japan.
The Trans-Siberian Railway is a network of railways connecting Moscow with the Russian Far East and the Sea of Japan. It is the longest railway in the world.
Baldwin Street in New Zealand holds the Guinness World Record for the steepest street. It has a gradient of 35% at its steepest point, making it quite a challenging climb for visitors.
Rand railway line was created in 1920.