\documentclass{paper}
\usepackage{amsmath}
\begin{document}
\begin{equation}
orientation =
\begin{cases}
horizontal & \text{if } \lvert slope \rvert < \frac{1}{threshold_{slope}} \\
vertical & \text{if } \ vert slope \rvert > threshold_{slope} \\
neither & \text{otherwise}\\
\end{cases}
\label{eq:slopethresh}
\end{equation}
\end{document}

