Anons, I have a dumb question. Really dumb. But bear with me. I need to prove some simple linearity properties, such as f(a+b) = f(a) + f(b). So I tried a simple linear equation y=2x+3, and then a=1 and b=1, so f(a+b) = 2(1+1) + 3 = 7, but f(a) + f(b) = 5+5=10. What am I doing wrong?
Isn't y=ax+b a linear function?? The reasoning above would only make sense if b=0, correct?

Just googled this and apparently ax+b is NOT a linear function. It is an "affine" function. Whatever that means. My world just collapsed. Literally. I thought I understood linearity intuitively. What is wrong here?? How is it non linear if it is literally a line? A non-linear line??