If , then for some real m.

Proof:

Setting and , we have ;

in other words .

Next, set and , which yields .

Since , we have , or

.

Let (the left side)

Then we see that and is an odd function, i.e. .

Now,

but also

Setting equal the right sides of the above two equations and simplifying,

we get

,

which is the definition of linear function with . (y-intercept = 0)