So for every units you have gone to the right, you have gone units down.
This would suggest that this line would have direction the same as .
But we don't know the length of this vector. So multiply the vector by some parameter .
Therefore the vector that goes in the direction of this line that also has the same length as this line can be written as
Now we just need a point that lies on the line so we know where to place this vector. The intercept will suffice.
Therefore, the vector form of this line is
or if you like