Given the function $f\left(x\right)=-5+7x$, identify its inverse function from the following options. Then, graph the function and its inverse.

$f^{-1}\left(x\right)=\frac{1}{7}x-\frac{5}{7}$

$f^{-1}\left(x\right)=\frac{1}{7}x+\frac{5}{7}$

$f^{-1}\left(x\right)=\frac{1}{7}x+5$

$f^{-1}\left(x\right)=\frac{1}{7}x-5$