1. **State the problem:** We have a linear function with inputs and outputs given as pairs: input: 1, 2, 3, 4 and output: 7, 9, 11, 13. We need to find the output when the input is $n$. 2. **Identify the pattern:** Notice the outputs increase by 2 each time as the input increases by 1. This suggests a linear function of the form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{\text{change in output}}{\text{change in input}} = \frac{9 - 7}{2 - 1} = \frac{2}{1} = 2$$ 4. **Find the y-intercept $b$:** Use one point, for example input 1 and output 7: $$7 = 2 \times 1 + b \implies b = 7 - 2 = 5$$ 5. **Write the function rule:** $$y = 2x + 5$$ 6. **Find the output when input is $n$:** $$y = 2n + 5$$ **Final answer:** The output when the input is $n$ is $$\boxed{2n + 5}$$.