1. The problem is to understand the definition and relationship between two lines in geometry. 2. Two lines can be related in several ways: they can be parallel, intersecting, or coincident. 3. **Parallel lines** are lines in the same plane that never meet, no matter how far they are extended. They have the same slope. 4. **Intersecting lines** cross each other at exactly one point. Their slopes are different. 5. **Coincident lines** are lines that lie exactly on top of each other, meaning they have all points in common. 6. The slope formula for a line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$m=\frac{y_2-y_1}{x_2-x_1}$$ 7. To check if two lines are parallel, compare their slopes. If $m_1 = m_2$, the lines are parallel. 8. To check if two lines intersect, their slopes must be different: $m_1 \neq m_2$. 9. If two lines have the same slope and the same y-intercept, they are coincident. This explanation covers the basic definitions and relationships between two lines.