1. **State the problem:** We are given a table with values of $x$ and $y$: $$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ y & 5 & 10 & 15 & 20 \\ \end{array}$$ We need to determine which two statements correctly describe the relationship between $x$ and $y$. 2. **Analyze the pattern:** Look at how $y$ changes as $x$ increases. - When $x=1$, $y=5$ - When $x=2$, $y=10$ - When $x=3$, $y=15$ - When $x=4$, $y=20$ 3. **Check for multiplicative pattern:** Calculate $\frac{y}{x}$ for each pair: $$\frac{5}{1} = 5, \quad \frac{10}{2} = 5, \quad \frac{15}{3} = 5, \quad \frac{20}{4} = 5$$ Since $\frac{y}{x}$ is constant, the relationship is multiplicative. 4. **Write the equation:** $$y = 5x$$ 5. **Check the given statements:** - A: $x = 5y$ (incorrect, should be $y=5x$) - B: $y = x + 5$ (incorrect, pattern is multiplicative, not additive) - C: $x = y + 5$ (incorrect, no such pattern) - D: $y = 5x$ (correct, matches our equation) - E: $y = x + 5$ (incorrect, additive pattern not matching data) - F: $y = 5x$ (correct, same as D) 6. **Conclusion:** The two correct statements are D and F.