1. **Problem Statement:** Given the sequence -2, 7, 16, 25, 34, find the formula the engineer used to determine the assigned values, where $n$ is the number of times the program was run. 2. **Identify the pattern:** Calculate the differences between consecutive terms: $7 - (-2) = 9$ $16 - 7 = 9$ $25 - 16 = 9$ $34 - 25 = 9$ The common difference is 9, indicating an arithmetic sequence. 3. **General formula for arithmetic sequence:** $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. 4. **Apply values:** $$a_n = -2 + (n-1)9 = -2 + 9n - 9 = 9n - 11$$ 5. **Answer for Part A:** The formula is $a_n = 9n - 11$, which corresponds to option A. --- 6. **Problem Statement for Part B:** Graph the inequality $y > \frac{3}{4}x + 5$ and complete the table with details for graphing. 7. **Identify slope and y-intercept:** The inequality is in slope-intercept form $y = mx + b$ where: - Slope $m = \frac{3}{4}$ - y-intercept $b = 5$ 8. **Line type:** Since the inequality is strict ($>$), the boundary line is **dashed**. 9. **Shading:** Because the inequality is $y > \frac{3}{4}x + 5$, shade the region **above** the line. 10. **Summary Table:** - Slope: $\frac{3}{4}$ - y-intercept: 5 - Line: Dashed - Shading: Above --- **Final answers:** **Part A:** $a_n = 9n - 11$ **Part B:** Slope = $\frac{3}{4}$ Y-intercept = 5 Line = Dashed Shading = Above