1. **State the problem:** Find the value of $k$ such that the lines $5x + 2y + 6 = 0$ and $15x + ky - 10 = 0$ are parallel. 2. **Recall the rule for parallel lines:** Two lines $Ax + By + C = 0$ and $A'x + B'y + C' = 0$ are parallel if and only if their slopes are equal, i.e., $\frac{-A}{B} = \frac{-A'}{B'}$. 3. **Find the slope of the first line:** For $5x + 2y + 6 = 0$, rearranged as $2y = -5x - 6$, slope $m_1 = -\frac{5}{2}$. 4. **Find the slope of the second line:** For $15x + ky - 10 = 0$, rearranged as $ky = -15x + 10$, slope $m_2 = -\frac{15}{k}$. 5. **Set slopes equal for parallelism:** $$-\frac{5}{2} = -\frac{15}{k}$$ 6. **Solve for $k$:** $$\frac{5}{2} = \frac{15}{k} \implies 5k = 2 \times 15 \implies 5k = 30 \implies k = \frac{30}{5} = 6$$ **Final answer:** $k = 6$