1. **State the problem:** We have a table of ordered pairs for a linear function with inputs 1, 2, 3, 4 and corresponding outputs 9, 13, 17, 21. We need to find the output when the input is $n$. 2. **Identify the pattern:** The function is linear, so the output changes by a constant amount as the input increases by 1. 3. **Calculate the rate of change (slope):** $$\text{slope} = \frac{13 - 9}{2 - 1} = \frac{4}{1} = 4$$ This means for each increase of 1 in input, output increases by 4. 4. **Find the function rule:** The function can be written as: $$f(x) = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 5. **Find $b$ using a known point:** Using input 1 and output 9: $$9 = 4 \times 1 + b$$ $$b = 9 - 4 = 5$$ 6. **Write the function rule:** $$f(x) = 4x + 5$$ 7. **Find the output when input is $n$:** $$f(n) = 4n + 5$$ **Final answer:** The output when the input is $n$ is $$\boxed{4n + 5}$$.