Answer
$(x_0,mx_0+b)$
Work Step by Step
As we know that $y=mx+b$
Now, at any point $(x_0,mx_0+b)$, we have: $y'=\lim\limits_{h\to0}\dfrac{m(x_0+h)+b-(mx_0+b)}{h}=\lim\limits_{h\to0}\dfrac{mx_0+mh+b-mx_0-b}{h}=\lim\limits_{h\to0}\dfrac{mh}{h}=m$
Thus, the tangent line at any point $x=x_0$ can be written as:$y=mx+n$
Next, consider point $(x_0,mx_0+b)$:
$mx_0+n=mx_0+b \implies n=b$
So, the tangent line of the given line is $y=mx+b$ will be remained as the same line.
Hence, this implies that the line $y=mx+b$ has its own tangent line at the point $(x_0,mx_0+b)$.
