1. **State the problem:** We have a linear function with inputs and outputs given as: | Input | 1 | 2 | 3 | 4 | n | |-------|---|---|---|---|---| | Output| -9| -12| -15| -18| ? | We need to find the output when the input is $n$. 2. **Identify the pattern:** Since the function is linear, the output changes by a constant amount when the input increases by 1. 3. **Calculate the common difference:** $$-12 - (-9) = -3$$ $$-15 - (-12) = -3$$ $$-18 - (-15) = -3$$ The output decreases by 3 for each increase of 1 in input. 4. **Find the function rule:** Let the function be $f(x) = mx + b$. Using input 1 and output -9: $$f(1) = m(1) + b = -9$$ Using input 2 and output -12: $$f(2) = 2m + b = -12$$ Subtract the first equation from the second: $$\cancel{2m} + b - (\cancel{m} + b) = -12 - (-9)$$ $$m = -3$$ 5. **Find $b$:** From $f(1) = m + b = -9$: $$-3 + b = -9$$ $$b = -9 + 3 = -6$$ 6. **Write the function:** $$f(x) = -3x - 6$$ 7. **Find output for input $n$:** $$f(n) = -3n - 6$$ **Final answer:** The output when the input is $n$ is $$\boxed{-3n - 6}$$