1. **State the problem:** We are given a table showing a proportional relationship between $x$ and $y$: | x | 0.5 | 1 | 1.5 | 2 | | y | 20.5 | 41 | 61.5 | 82 | We need to write the equation of the form $y = kx$ that represents this relationship. 2. **Recall the formula:** A proportional relationship means $y$ is directly proportional to $x$, so: $$y = kx$$ where $k$ is the constant of proportionality. 3. **Find $k$ using one pair of values:** Using $x=1$ and $y=41$: $$41 = k \times 1$$ So, $$k = 41$$ 4. **Verify $k$ with other points:** For $x=0.5$, $y$ should be: $$y = 41 \times 0.5 = 20.5$$ which matches the table. For $x=1.5$, $$y = 41 \times 1.5 = 61.5$$ For $x=2$, $$y = 41 \times 2 = 82$$ All match the table, confirming $k=41$. 5. **Write the equation:** $$\boxed{y = 41x}$$