1. **State the problem:** Manny can put together 3 airplane models in 4.5 hours and 4 models in 6 hours. We need to find the time it takes to put together 1 model, write an equation for time $y$ based on number of models $x$, and find the time for 8 models. 2. **Fill in the table:** Given values: Number of models (x) | Total time in hours (y) 1 | ? 2 | ? 3 | 4.5 4 | 6 3. **Calculate the unit rate (time per model):** We find the rate using the two points (3, 4.5) and (4, 6). Calculate the rate of change (slope): $$\text{slope} = \frac{6 - 4.5}{4 - 3} = \frac{1.5}{1} = 1.5$$ This means it takes 1.5 hours per model. 4. **Find time for 1 model:** Using the point (3, 4.5), check if consistent: $$4.5 = 3 \times 1.5$$ This matches, so unit rate is 1.5 hours per model. 5. **Write the equation:** Time $y$ is proportional to number of models $x$: $$y = 1.5x$$ 6. **Fill in missing table values:** For $x=1$: $$y = 1.5 \times 1 = 1.5$$ For $x=2$: $$y = 1.5 \times 2 = 3$$ 7. **Calculate time for 8 models:** $$y = 1.5 \times 8 = 12$$ **Final answer:** It will take Manny 12 hours to put together 8 airplane models.