Answer
The ray can be parametrized with
$\left\{\begin{array}{l}
x=-1+t\\
y=-2t+2
\end{array}\right.\qquad t \geq 0$
Work Step by Step
A point-slope equation of a line passing through (a,b) is
$y-b=m(x-a)$.
In this problem, $(a,b)=(-1,2)$ and $m=\displaystyle \frac{0-2}{0-(-1)}=-2$
We can define the parameter $t$ so that $t=x-a$,
so a set of parametric equations could be $\left\{\begin{array}{l}
x=a+t\\
y=mt+b
\end{array}\right.$,
so the line can be parametrized with $\left\{\begin{array}{l}
x=-1+t\\
y=-2t+2
\end{array}\right.$
We need just the half line (the ray).
$(-1,2)$ is on the line for $t=0,$
$(0,0)$ is on the line for $t=1,$ (positive t)
so the ray can be parametrized with
$\left\{\begin{array}{l}
x=-1+t\\
y=-2t+2
\end{array}\right.\qquad t \geq 0$
