change position to get graph and equation at the same level - RMarkdown / .tex

Question

I am creating a presentation in RMarkdown and in the slide below I want to put the graph on the left (with title above "Graph") and the couple of equations on the right, not below (with titte "Equations") - how to do this? Re the couple of questions, M: should appear first in the middle, and then the 4 equations.

Here is the slide with current output:

Here is the code in RMarkdown for that specific slide:

---
title: title

author: name
        
date: "`r format(Sys.time(), '%d %B %Y')`"

output:
  beamer_presentation:
    theme: Szeged
    slide_level: 2
    includes:
      in_header: header.tex
    keep_tex: true

linkcolor: false
---

## Model

\small
\justify
A line of text goes here:

\begin{tikzpicture}[>=triangle 45, font=\footnotesize]
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={above:{T}}] (T) at (0,0) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={above:{Y}}] (Y) at (4,0) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={below:{X}}] (X) at (2,1) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={above:{W}}] (W) at (0,1.5) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={below:{$U_T$}}] (UT) at (0,-1) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={below:{$U_Y$}}] (UY) at (4,-1) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={above:{$U_X$}}] (UX) at (2,2) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={below:{$U_W$}}] (UW) at (-1,1.5) {};
\draw[->,shorten >= 1pt] (X)--(T);
\draw[->,shorten >= 1pt] (X)--(Y);
\draw[->,shorten >= 1pt] (W)--(X);
\draw[->,shorten >= 1pt] (UT)--(T);
\draw[->,shorten >= 1pt] (UY)--(Y);
\draw[->,shorten >= 1pt] (UX)--(X);
\draw[->,shorten >= 1pt] (UW)--(W);
\end{tikzpicture}

$M:$
$W := f_W (\epsilon_W)$  
$X := f_X (W, \epsilon_X)$  
$T := f_T (X, \epsilon_T)$  
$Y := f_Y (X, \epsilon_Y)$  

\small
\justify
A final line of text here.

Here is the code for the header.tex:

\definecolor{mycolorlightblue}{RGB}{103,153,200}
\definecolor{mycolordarkblue}{RGB}{0,70,127}
% add packages
\usepackage{tikz}
\usetikzlibrary{arrows}
\usepackage{tcolorbox}
\usepackage{ragged2e}
% remove 2nd section from header
\makeatletter
\beamer@theme@subsectionfalse
\makeatother
% change colour of lines
\setbeamercolor{separation line}{bg=mycolorlightblue}
% text title
\setbeamercolor{title}{fg=mycolordarkblue}
\setbeamercolor{frametitle}{fg=mycolordarkblue}
% text colour
\setbeamercolor{frametitle}{fg=mycolordarkblue}
% item colour
\setbeamercolor{structure}{fg=mycolordarkblue}
% no header or footer on first page
\thispagestyle{empty}
% remove title slides at beginning of sections
\AtBeginSection{}
% add page counter to the footer
\setbeamertemplate{footline}[frame number]
% logo of my university
\titlegraphic{%
  \begin{picture}(0,0)
    \put(155,0){\makebox(0,0)[rt]{\includegraphics[]{ALL-ICONS.png}}}
  \end{picture}}

Answer 1

As you are not using anything markdown specific in your columns, you can use the beamer columns environment:

---
title: title

author: name
        
date: "`r format(Sys.time(), '%d %B %Y')`"

output:
  beamer_presentation:
    theme: Szeged
    slide_level: 2
    includes:
      in_header: header.tex
    keep_tex: true

linkcolor: false
---

## Model

\small
\justifying
A line of text goes here:

\begin{columns}[T,onlytextwidth]
\begin{column}{.45\textwidth}
\begin{tikzpicture}[>=triangle 45, font=\footnotesize]
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={above:{T}}] (T) at (0,0) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={above:{Y}}] (Y) at (4,0) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={below:{X}}] (X) at (2,1) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={above:{W}}] (W) at (0,1.5) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={below:{$U_T$}}] (UT) at (0,-1) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={below:{$U_Y$}}] (UY) at (4,-1) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={above:{$U_X$}}] (UX) at (2,2) {};
\node[fill,circle,inner sep=0pt,minimum size=5pt,label={below:{$U_W$}}] (UW) at (-1,1.5) {};
\draw[->,shorten >= 1pt] (X)--(T);
\draw[->,shorten >= 1pt] (X)--(Y);
\draw[->,shorten >= 1pt] (W)--(X);
\draw[->,shorten >= 1pt] (UT)--(T);
\draw[->,shorten >= 1pt] (UY)--(Y);
\draw[->,shorten >= 1pt] (UX)--(X);
\draw[->,shorten >= 1pt] (UW)--(W);
\end{tikzpicture}
\end{column}
\begin{column}{.45\textwidth}
$M:$
$W := f_W (\epsilon_W)$  
$X := f_X (W, \epsilon_X)$  
$T := f_T (X, \epsilon_T)$  
$Y := f_Y (X, \epsilon_Y)$  
\end{column}
\end{columns}

\small
\justifying
A final line of text here.