\documentclass[10pt]{article}
\usepackage{pgf,tikz,pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}

\begin{tikzpicture}[x=1cm,y=1cm]
\begin{axis}[
x=1cm,y=1cm,
axis lines=middle,
ymajorgrids=true,
xmajorgrids=true,
xmin=-0.5,
xmax=7.5,
ymin=-1,
ymax=2.5,
xtick={0,...,7},
ytick={0,...,3},]
\clip(-0.5327923283402358,-3.438438462661708) rectangle (7.550357053950259,3.4379509853468746);
\draw [-latex,line width=1pt] (0,0) -- (5,0);
\draw [-latex,line width=1pt] (0,0) -- (2,2);
\draw [-latex,line width=1pt,color=red, dashed] (2,2) -- (7,2);
\draw [-latex,line width=1pt,color=red, dashed] (5,0) -- (7,2);
\draw [-latex,line width=1pt,color=blue] (0,0) -- (7,2);
\begin{scriptsize}

\draw[color=black] (2.55908371629915,-0.25) node {$\vec{y}$};

\draw[color=black] (0.8,1.1993756042973518) node {$\vec{x}$};

\draw[color=red] (4.315669182768639,2.3) node {$\vec{y}$};
\draw[color=red] (6.45,1.142250873680458) node {$\vec{x}$};
\draw[color=blue] (3.1,1.220797378278687) node {$\vec{x+y}$};
\end{scriptsize}
\end{axis}
\end{tikzpicture}
\end{document}