True/false If f is a linear function then f(r+s)= f(r)+f(s)

Question

True false not enough information . Need steps please

Answer 1

let f(x) = mx + b

 

f(r+s) = m(r+s) + b = mr + ms + b

 

f(r) + f(s) = mr + b + ms + b = mr + ms +2b

 

THIS PROVES THAT THE ANSWER IS FALSE, in general, although if b=0 it is true.