The question asks to express $y$ in terms of $x$ and $k$, where $y$ is directly proportional to $x$, and $k$ is a constant of proportionality.

When two quantities are directly proportional, they have the relationship:

$y = kx$

Thus, the correct option is 4. $y = kx$.

Would you like further clarification on the concept? Here are some related questions to deepen your understanding:

1. What is the difference between direct and inverse proportionality?
2. How would the equation change if $y$ were inversely proportional to $x$?
3. Can you give an example of a real-world situation where two variables are directly proportional?
4. How can you determine the constant of proportionality $k$ if you are given specific values for $x$ and $y$?
5. What happens to $y$ when $x$ doubles, assuming $y$ is directly proportional to $x$?

Tip: When variables are directly proportional, increasing one leads to a proportional increase in the other, based on the constant $k$.