p = k 4 j + 9 The given equation relates the distinct positive numbers p

Choice A is correct. To express $4j+9$ in terms of $p$ and $k$, the given equation must be solved for $4j+9$. Since it's given that $j$ is a positive number, $4j+9$ is not equal to zero. Therefore, multiplying both sides of the given equation by $4j+9$ yields the equivalent equation $p\left(4j+9\right)=k$. Since it's given that $p$ is a positive number, $p$ is not equal to zero. Therefore, dividing each side of the equation $p\left(4j+9\right)=k$ by $p$ yields the equivalent equation $4j+9=\frac{k}{p}$.

Choice B is incorrect. This equation is equivalent to $p=\frac{4j+9}{k}$.

Choice C is incorrect. This equation is equivalent to $p=k-4j-9$.

Choice D is incorrect. This equation is equivalent to $p=k\left(4j+9\right)$.