Explanation:

To understand the number of parallel lines that can be drawn passing through a point not on the given line, we need to consider the concept of parallel lines and their properties.

Parallel Lines:
Parallel lines are lines that never intersect, no matter how far they are extended. They have the same slope and are always equidistant from each other.

Properties of Parallel Lines:
1. Parallel lines have the same slope.
2. Parallel lines are always equidistant from each other.
3. Parallel lines never intersect.

Analysis:
In the given question, we are asked to determine the number of parallel lines that can be drawn passing through a point not on the given line.

Let's consider a line (L) and a point (P) not on this line.

Case 1: Line L is vertical:
If the given line (L) is vertical, it means its slope is undefined. In this case, only one line can be drawn passing through point P, which is the vertical line itself. So, the answer is 1.

Case 2: Line L is not vertical:
If the given line (L) is not vertical, it means its slope is defined. In this case, we can draw infinitely many parallel lines passing through point P.

To understand this, let's consider a point (P) and two parallel lines (L1 and L2) passing through P. Since L1 and L2 are parallel, they have the same slope.

Now, if we draw another line (L3) passing through P, it will either intersect L1 or L2 at some point. This violates the property of parallel lines, which states that parallel lines never intersect.

Therefore, we can conclude that only one parallel line can be drawn passing through a point not on the given line if the line is not vertical.

Conclusion:
In conclusion, the correct answer is option 'B' - 1. Only one parallel line can be drawn passing through a point not on the given line.