Traffic with constant density, $\rho_0$, is stopped by a red light at $x=0$. If $v(\rho)=1-\rho$, calculate what happends behind the light.
Unfortunately the main focus of this example in my notes wasn't on the space-time diagram so they provide the graph https://i.stack.imgur.com/XgA65.jpg without much explanation except for "Characteristics are given by $x=(1-2\rho)t+s$" and "Characteristics always intersect at $x=0$, $t=0$ for $0<\rho_0<1$". (Then after dealing with the shock, the graph https://i.stack.imgur.com/jHdSh.jpg. The shock isn't really the focus of my question though because I'm not far into the problem when it comes to my understanding of it)
What I'm not understanding is how the characteristics I'm seeing in the first graph are coming from $x=(1-2\rho)t+s$. For instance for $x<0$ the graph suggests the characteristics have positive gradient but if $\rho_0=\frac{3}{4}$ we have $x=-\frac{1}{2}t+s$ so $\frac{dt}{dx}=-2$ which is negative.
EDIT: Also, where does $\rho=1$ come from?
If someone could please answer my question I would greatly appreciate it!