Weird horizontal spacing after displayed equation

Question

As you can see, this is an excerpt from a submission to a journal. I am using the {\small } command to fit the equation into one line, albeit at the expense of its number falling onto the next line.

The problem is this undesired space at the beginning of the line right after the displayed equation. Clearly, using \hspace is not a good practice.

\documentclass[12pt]{article}
\usepackage{e-jc}
\usepackage{amsmath,mathtools}
\begin{document}
\begin{proof}
{\small
\begin{equation}
\label{eqn:lemma_proof}
    k
    =
    \frac{ f(b) - f(a) }{ g(b) - g(a) }
    \quad
    \text{and}
    \quad
    \ell
    =
    \frac{ f(a) g(b) - f(b) g(a) }{ g(b) - g(a) }
    =
    \frac{ f(c) g(b) - f(c) g(a) - f(b) g(c) + f(a) g(c) }{ g(b) - g(a) },
\end{equation}
}
%\hspace{-4mm}
where the last equality follows from
We can easily
verify that $R(a)=R(b)=0$ and $R(c)=0$ by using the first representation for
$\ell$ and the second representation for $\ell$, respectively.
\end{proof}
\end{document}