1. The problem is to understand and draw a parallel line. 2. Parallel lines are lines in a plane that never meet; they are always the same distance apart. 3. The key property is that parallel lines have the same slope if represented in coordinate geometry. 4. For example, if a line has equation $y = mx + b$, a line parallel to it will have equation $y = mx + c$ where $c \neq b$. 5. This means the two lines have the same slope $m$ but different intercepts. 6. Drawing a parallel line involves creating a line with the same slope but shifted up or down. 7. In the diagram, the original line and the parallel line are shown with equal spacing and no intersection. 8. This visual helps understand the concept of parallelism in geometry.