Determine the slope and write the Cartesian equation of the line. Write the equation of the line by the origin of coordinates that has vector director of components (1,2)  determine the slope and write the Cartesian equation of the line.
My attempt:
Let $l$ a line such that pass for the origin. 
Let $a$ a director vector of $l$. we know  as $a$ is a director vector of $l$ then the components $(1,2)$ are in the line.
We have two points of the line.
We know the general equation for the line is $Ax+By+C=0$
Here i'm stuck can someone help me?

A directing vector of a line is a vector which is collinear to any vector formed by two points on this line. 
Now take the point $O(0,0)$ which belongs to the line (as given) and any point $M(x, y) $ on this line. Thus the vector $OM$ is collinear to $(1,2)$; meaning that there exists a real number $k$ such that $OM=$k$a$.
Thus, by comparing their coordinates, we get: $x=k$ and $y=2k$, and thus $y=2x$ is the equation of this line (or $2x-y=0$).
