1. **State the problem:** We have a table showing input-output pairs and want to find the relationship between "In" and "Out" values. 2. **Given data:** | In | Out | |----|-----| | 24 | 7 | | 20 | 6 | | 16 | 5 | | 12 | 4 | | 12 | 3 | 3. **Observe the pattern:** As "Out" decreases by 1, "In" decreases by 4. 4. **Formulate the linear relationship:** Assume the function is linear: $$Out = m \times In + b$$ where $m$ is the slope and $b$ is the intercept. 5. **Calculate the slope $m$:** $$m = \frac{\Delta Out}{\Delta In} = \frac{6 - 7}{20 - 24} = \frac{-1}{-4} = \frac{1}{4}$$ 6. **Find the intercept $b$ using one point, e.g., $(In, Out) = (24, 7)$:** $$7 = \frac{1}{4} \times 24 + b \implies 7 = 6 + b \implies b = 1$$ 7. **Write the function:** $$Out = \frac{1}{4} In + 1$$ 8. **Verify with another point:** For $In=20$, $$Out = \frac{1}{4} \times 20 + 1 = 5 + 1 = 6$$ which matches the table. **Final answer:** $$Out = \frac{1}{4} In + 1$$