1. **Stating the problem:** Given that $y \propto x$ and $Y \propto \frac{1}{z}$, find the proportionality relation for $y$ in terms of $x$ and $z$. 2. **Recall the meaning of proportionality:** - $y \propto x$ means $y = kx$ for some constant $k$. - $Y \propto \frac{1}{z}$ means $Y = \frac{c}{z}$ for some constant $c$. 3. **Analyze the problem:** Since $y$ is proportional to $x$ and $Y$ is proportional to $\frac{1}{z}$, if $y$ and $Y$ represent the same quantity or are related, then combining these gives: $$y \propto x \quad \text{and} \quad y \propto \frac{1}{z}$$ 4. **Combine proportionalities:** When a variable is proportional to two quantities, it is proportional to their product or quotient depending on the relation. Here, since $y$ is proportional to $x$ and inversely proportional to $z$, we get: $$y \propto \frac{x}{z}$$ 5. **Answer:** The correct proportionality is $y \propto \frac{x}{z}$. **Therefore, the answer is option (b) $\frac{z}{x}$ is incorrect; the correct choice is $\frac{x}{z}$.**