The question asks which equation has a constant of proportionality equal to $\frac{1}{2}$. The constant of proportionality in a linear equation of the form $y = mx$ is the coefficient of $x$, which is $m$.

Let's analyze the options:

• A: $y = 2x$ — The constant of proportionality here is 2.
• B: $y = 4x$ — The constant of proportionality is 4.
• C: $y = \frac{3}{6}x$ — Simplifying $\frac{3}{6}$, we get $y = \frac{1}{2}x$, so the constant of proportionality is $\frac{1}{2}$.
• D: $y = \frac{3}{4}x$ — The constant of proportionality is $\frac{3}{4}$.

So, the correct answer is C: $y = \frac{3}{6}x$, as this equation simplifies to $y = \frac{1}{2}x$, with a constant of proportionality of $\frac{1}{2}$.

Would you like more details or have any further questions?

Here are five questions to expand on this concept:

1. What does the constant of proportionality represent in a linear equation?
2. How do you simplify fractions in an equation?
3. Can constants of proportionality be negative? If so, what does that imply?
4. How would you graph a line with a constant of proportionality equal to 1/2?
5. How can you determine the constant of proportionality from a table of values?

Tip: The constant of proportionality can be seen as the "rate of change" or "slope" in a linear equation, which determines how quickly $y$ changes with respect to $x$.