Transforming a Linear Programming Problem Into Standard Form

It is important for the creation of algorithms (for example Simplex Method) to have a standard form given by

Standard LP

$$\underset{x\in {\mathbb{R}}^n}{\min }{c}^{T}xs.t.\{\begin{array}{l}Ax=b\\ x\ge 0\end{array}$$Link to original

However this is not always the case, and is often on the form

$$\underset{x\in {\mathbb{R}}^n}{\min }{c}^{T}xs.t.Ax\le b$$

This is solved using a Slack Variable