.

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

.