Help me understand linear function. today in my high school lesson I learned for linear function. I know that each linear function has the form of $f(x)=kx+n$ where $k,x,n ∈ \mathbb R$. Now let's say be have those two functions:
$f_1(x)=kx+n_1\\
f_2(x)=kx+ n_2$
Since $k$ is same in both functions, we know that it represents those function whose graph will be parallel, but why and how to prove that those functions will be parallel?

Suppose $n_1 \ne n_2$.  If there was a value $x=a$ where $f_1(a) = f_2(a)$ then $ka+n_1 = ka+n_2$.  But then $n_1=n_2$ which is a contradiction.
