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. **Identify the pattern:** The inputs are $1, 2, 3, 4$ and the corresponding outputs are $4, 7, 10, 13$. 3. **Find the rule:** Notice the output increases by $3$ each time the input increases by $1$. This suggests the function is linear with a slope of $3$. 4. **Write the function rule:** A linear function can be written as $$f(x) = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 5. **Calculate the slope $m$:** $$m = \frac{7 - 4}{2 - 1} = \frac{3}{1} = 3$$ 6. **Find the y-intercept $b$:** Use one point, for example $(1,4)$: $$4 = 3 \times 1 + b \implies b = 4 - 3 = 1$$ 7. **Write the final function:** $$f(x) = 3x + 1$$ 8. **Find the output when input is $n$:** $$f(n) = 3n + 1$$ **Answer:** The output for input $n$ is $3n + 1$.