If y2 is inversely proportional to x, write down the equation connecting x, y and a constant k. y2  =

Break Down the Problem

1. Identify the relationship: Since $y^2$ is inversely proportional to $x$, we understand that as $x$ increases, $y^2$ decreases and vice versa.

Relevant Concepts

2. Express the relationship mathematically: If a variable $y^2$ is inversely proportional to $x$, we can write this as: $y^2 = \frac{k}{x}$ where $k$ is a constant of proportionality.

Analysis and Detail

3. The constant $k$ reflects the effect of $x$ on $y^2$. We can say that:
   • For a given value of $k$, if $x$ increases, $y^2$ will decrease correspondingly.
   • Conversely, if $x$ decreases, $y^2$ will increase.

Verify and Summarize

4. This inverse relationship captures the essence of how two variables interact. In this case, you can recall that the relationship is strictly true under the definition of inverse proportionality.

Final Answer

Thus, the equation connecting $x$, $y$, and the constant $k$ is: $y^2 = \frac{k}{x}$