Curves as graph of a function

Question

Let $u: [a,b]\in\mathbb{R}\rightarrow \mathbb{R}^2$ be a continuous and lipschitz curve (it means that $||u(t_1)-u(t_2)||\le C|t_1-t_2|$ for all $t_1,t_2\in [a,b]$)such that $u(a)=(0,0), u(b)=(x,y), x>0,y\le 0$. Can we parametrize $u$ as a graph of a continuous decreasing function w from $[0,x]$ to $\mathbb{R}$?