What is the geometric interpretation of the constant c/||n||? (vectors) [See part (e) of the attache image]

Part (e) of the question attached: Find the geometric interpretation of the constant c/||n||, when both sides of the cartesian equation x•n=c is divided by the norm ||n|| of the vector n. 

I understand how they obtained the equivalent Cartesian equation but am struggling to understand the geometric interpretation of the constant (on the RHS).

Question Part (e)
Hopefully you get to see this before your class, but try multiplying the dot product so you get to a Cartesian description of a line. From that, it should be easy to see what the constant means.
Hopefully you get to see this before your class, but try multiplying the dot product so you get to a Cartesian description of a line. From that, it should be easy to see what the constant means.