<s>[INST] If $f(x) =mx$, then $f(a + b) = f(a) + f(b)$ for all $a$ and $b$? 
If $f(x) =mx$, then $f(a + b) = f(a) + f(b)$ for all $a$ and $b$. True or False.

Verification of work: I found a similar problem where $f(x)=y-mx+b$ and test values for $m$ and $b$ were used. $f(x)=y-mx+b$
My problem has $m$ and $x$ as the values so I worked it as such and came to the conclusion that the question is True. 
Give $m$ and $x$ the values of $3$ and $1$, respectively. So that, $f(x)=mx$ becomes $f(x)=(3)(1)$. 
Give $a$ and $b$ the values of $2$ and $4$. Now we have:
$$f(2)+f(4)=(3)(2)+(3)(4)=18$$
$$f(2+4)=f(6)=(3)(6)=18$$
$18=18,$ so that $f(x) =mx$, then $f(a + b) = f(a) + f(b)$
 [/INST] So if $f(x) = mx$, $f(a+b) = m(a+b) = ma + mb = f(a) + f(b)$
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