The question in the image asks to find the value of $k$, given that:

$f(x) = kx + 8, \quad \text{and} \quad f(2) = 0.$

Step-by-Step Solution:

1. The function is $f(x) = kx + 8$.
2. It is given that $f(2) = 0$, which means: $k(2) + 8 = 0.$
3. Simplifying the equation: $2k + 8 = 0.$
4. Subtract 8 from both sides: $2k = -8.$
5. Divide both sides by 2: $k = -4.$

Thus, the value of $k$ is $\boxed{-4}$.

Let me know if you'd like more details or have any questions!

Here are 5 follow-up questions you might find interesting:

1. What would the value of $f(x)$ be when $x = 5$?
2. How would the equation change if $f(3) = 0$ instead?
3. What happens to the function if $k = 0$?
4. How would you graph the function $f(x) = kx + 8$?
5. What is the significance of the slope $k$ in linear functions?

Tip: When solving for constants in functions, substituting given points into the equation can often simplify the process!