2. On a separate sheet of paper, sketch a graph of the inverse of $k(x)=\frac{7}{2} x-8$. Determine the $y$-intercept of $k^{-1}(x)$.

Step 1 ：The inverse of a function $f(x)$ is found by swapping the $x$ and $y$ values. This means that if $k(x)=\frac{7}{2} x-8$, then $k^{-1}(x)$ would be found by swapping $x$ and $y$ to get $x=\frac{7}{2} y-8$.

Step 2 ：Solving this equation for $y$ will give us the equation of $k^{-1}(x)$.

Step 3 ：The $y$-intercept of a function is the $y$ value when $x=0$. So, to find the $y$-intercept of $k^{-1}(x)$, we need to substitute $x=0$ into the equation of $k^{-1}(x)$.

Step 4 ：After substituting $x=0$ into the equation, we get $y=2.28571428571429$.

Step 5 ：So, the $y$-intercept of $k^{-1}(x)$ is $2.28571428571429$.

Step 6 ：Final Answer: The $y$-intercept of $k^{-1}(x)$ is \(\boxed{2.28571428571429}\).