Like this:

For such equations is in amsmath defined environment cases. For its numbering you should insert in equation environment as stated @Henri Menke in his comment:
\documentclass[12pt,a4paper]{article}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{xcolor} % <---
\begin{document}
\begin{equation}\color{blue!70!black} <---
\Phi_{1} =
\begin{cases}
a(x) & x\leq \frac{1}{3} \\
b(x) & x> \frac{1}{3} \\
\end{cases}
\end{equation}
\end{document}
Edit (1):
If you like to have only this equation in blue color, than after \begin{equation} add for example \color{blue!70!black}, as is added now in above MWE.
Edit (2):
However, if you like to have all math expressions colored, than two solutions are provided in answer of Stefan Kottwitz and in answer of David Carlisle. Considering them in above MWE, you will get:

and

respectively. Difference between them is color of equation numbers.
empheq. See e.g. https://tex.stackexchange.com/a/258879. – Apr 05 '20 at 06:19\begin{equation}...\end{equation}instead of\[...\]. – Henri Menke Apr 05 '20 at 06:20\usepackage{amsmath} \usepackage{empheq}
\begin{document} \begin{empheq}[left={\Phi_{1}=\empheqlbrace,}]{align} a(x);, &\quad\text{if}~ x\leq \frac{1}{3};, \notag\ b(x);, &\quad\text{if}~x> \frac{1}{3} ;. \end{empheq} \end{document}`?
– Apr 05 '20 at 06:26amsmath <= mathtools. – Sebastiano Apr 05 '20 at 10:47