Proof: Direct Variation & Linear Function Not Equal to 0

[threetheoreom]

Homework Statement

I going thorough some of my old notes and I saw this question for a proof.

If f is linear function but not a direct variation and not the constant function 0, then for every pair of real numbers a and c
f(a + c) not equal to f(a)+f(c).

Homework Equations

y = mx ( a linear function ) m = y/x

The Attempt at a Solution

I can't seem to get the logic together, a linear function that is actually a direct variation produces contant distances on a number line, so i would think a function that isn't a direct variation would be map irregular dstances.

I would like some direction as to how connect this the fact that additive distribution doesn't hold for such functions.

thanks

edit: I meant this for the precal section.

 

[Dick]

Does this mean f(x) is a linear function of the form f(x)=a*x+b with b not equal to zero? (Is the case b=0 what you mean by a 'direct variation'?). In that case the proof is pretty easy. Just write out f(a+c) and f(a)+f(c) and compare them.

 

[threetheoreom]

Does this mean f(x) is a linear function of the form f(x)=a*x+b with b not equal to zero? (Is the case b=0 what you mean by a 'direct variation'?). In that case the proof is pretty easy. Just write out f(a+c) and f(a)+f(c) and compare them.

hmmm thanks.