How can the vertical number line be used to add or subtract

A vertical number line resembles a thermometer. It emphasizes that we count up in the number system. Vertical number lines are just alternative way to look at the numbers.

This is commonly used in adding or subtracting

For example: 5 - 3

5 is the start, the sign determines whether you go down or go up, the minus sign denotes down then so the last number denotes how many steps you are going down where you land is the answer. The same goes with addition but instead of down, the plus sign denotes going up.