1. **State the problem:** Determine if line j passing through points (10, 6) and (1, 4) and line k passing through points (10, 9) and (1, 7) are parallel, perpendicular, or neither. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate slope of line j:** $$m_j = \frac{4 - 6}{1 - 10} = \frac{-2}{-9} = \frac{\cancel{-2}}{\cancel{-9}} = \frac{2}{9}$$ 4. **Calculate slope of line k:** $$m_k = \frac{7 - 9}{1 - 10} = \frac{-2}{-9} = \frac{\cancel{-2}}{\cancel{-9}} = \frac{2}{9}$$ 5. **Compare slopes:** Since $m_j = m_k = \frac{2}{9}$, the lines have the same slope. 6. **Conclusion:** Lines with the same slope are parallel. **Final answer:** Lines j and k are parallel.