1. **State the problem:** We have two lines, Line A passing through points (3, 6) and (5, -2), and Line B passing through points (2, 5) and (8, k). We need to find the value of $k$ such that Line A and Line B are parallel. 2. **Formula and rule:** The slope of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Two lines are parallel if and only if their slopes are equal. 3. **Calculate slope of Line A:** $$m_A = \frac{-2 - 6}{5 - 3} = \frac{-8}{2} = -4$$ 4. **Calculate slope of Line B:** $$m_B = \frac{k - 5}{8 - 2} = \frac{k - 5}{6}$$ 5. **Set slopes equal for parallel lines:** $$m_A = m_B$$ $$-4 = \frac{k - 5}{6}$$ 6. **Solve for $k$:** Multiply both sides by 6: $$6 \times (-4) = 6 \times \frac{k - 5}{6}$$ $$-24 = \cancel{6} \times \frac{k - 5}{\cancel{6}}$$ $$-24 = k - 5$$ Add 5 to both sides: $$-24 + 5 = k - 5 + 5$$ $$-19 = k$$ **Final answer:** $$k = -19$$