1. **State the problem:** We are given a table of input-output pairs for a linear function and need to find the output when the input is $n$. 2. **Given table:** | Input | 1 | 2 | 3 | 4 | $n$ | |-------|---|---|---|---|-----| | Output| -3| -1| 1 | 3 | ? | 3. **Find the rule:** Since the function is linear, it follows a two-step rule of the form: $$\text{output} = a \times \text{input} + b$$ where $a$ and $b$ are constants. 4. **Calculate the rate of change $a$:** Between input 1 and 2: $$a = \frac{-1 - (-3)}{2 - 1} = \frac{2}{1} = 2$$ Check between input 2 and 3: $$a = \frac{1 - (-1)}{3 - 2} = \frac{2}{1} = 2$$ So the slope $a = 2$. 5. **Find $b$ by substituting one point:** Using input 1 and output -3: $$-3 = 2 \times 1 + b$$ $$b = -3 - 2 = -5$$ 6. **Write the function rule:** $$\text{output} = 2 \times \text{input} - 5$$ 7. **Find output when input is $n$:** $$\text{output} = 2n - 5$$ **Final answer:** The output for input $n$ is $$\boxed{2n - 5}$$