1. The problem involves understanding the relationship between variables $x$ and $y$ given two different values of $k$ and their corresponding data tables. 2. Typically, $k$ represents a constant of proportionality in equations like $y = kx$ or $y = \frac{k}{x}$. 3. For the first table with $k=0.2$, check if $y = kx$ holds: $$y = 0.2 \times x$$ Check for $x=2$: $y = 0.2 \times 2 = 0.4$, but given $y=10$, so $y \neq 0.2x$. 4. Try $y = \frac{k}{x}$: $$y = \frac{0.2}{x}$$ For $x=2$: $y = \frac{0.2}{2} = 0.1$, but given $y=10$, so no. 5. Try $y = kx^n$ for some $n$: Using points $(2,10)$ and $(4,20)$: $$10 = 0.2 \times 2^n$$ $$20 = 0.2 \times 4^n$$ Divide second by first: $$\frac{20}{10} = \frac{0.2 \times 4^n}{0.2 \times 2^n} = \frac{4^n}{2^n} = (\frac{4}{2})^n = 2^n$$ So: $$2 = 2^n \implies n=1$$ 6. So $y = 0.2 x$ should hold, but data shows otherwise. Check if $k$ is actually $\frac{y}{x}$: For $x=2$, $k=\frac{10}{2}=5$ not 0.2. 7. Similarly for the second table with $k=1.6$, check $k=\frac{y}{x}$: For $x=7.5$, $k=\frac{4.5}{7.5}=0.6$ not 1.6. 8. Conclusion: The given $k$ values do not match the ratio $\frac{y}{x}$ for the data points. 9. Possibly, $k$ is a parameter in a different model or the data is unrelated to $k$ as a proportionality constant. 10. Without further instructions, the problem is to verify if $y=kx$ holds for given $k$ and data, which it does not. Final answer: The data does not fit the model $y = kx$ for the given $k$ values.