1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the constant of proportionality $k$ such that $y = kx$. 2. **Formula and rules:** The formula for direct proportionality is: $$y = kx$$ where $k$ is the constant of proportionality. 3. **Use the given data:** From the table: $$x = 3, y = 2.7$$ Substitute into the formula: $$2.7 = k \times 3$$ 4. **Solve for $k$:** Divide both sides by 3: $$k = \frac{2.7}{3}$$ Show cancellation: $$k = \frac{\cancel{2.7}}{\cancel{3}} = 0.9$$ 5. **Verify with other points:** For $x=7$, $y=6.3$: $$6.3 = k \times 7$$ $$k = \frac{6.3}{7} = 0.9$$ For $x=10$, $y=9$: $$9 = k \times 10$$ $$k = \frac{9}{10} = 0.9$$ All points confirm $k=0.9$. **Final answer:** $$\boxed{0.9}$$