I was looking through the Wikipedia page of "Homogeneous functions" and it stated that any linear function that maps V onto W is homogeneous of degree one. However, when I try to apply the definition of a homogeneous function to a line defined by one variable "v" and a non-zero constant "z":
I find that the line is not homogeneous.
So why is it that a linear function is always homogeneous even though the example I gave shows that it's not? What conceptual/calculation mistake did I make in in the process?