Explanation:

When we have a line and a point not on that line, we can draw only one parallel line passing through that point. Let's understand why this is the case.

Definition of a Parallel Line:
Two lines are said to be parallel if they never intersect, no matter how far they are extended.

Proof:
To understand why only one parallel line can be drawn through a point not on a given line, let's consider two possibilities:

1. No parallel line:
If we cannot draw any parallel line through the given point, then the answer would be 0. However, this is not possible because we can always draw at least one line through any given point.

2. More than one parallel line:
Suppose we are able to draw two parallel lines through the given point. Let's call these lines 'l1' and 'l2'. Now, since 'l1' and 'l2' are parallel, they will never intersect. But this contradicts the definition of a parallel line.

According to the definition, two parallel lines should never intersect. If 'l1' and 'l2' are parallel and pass through the same point, they must intersect at that point. Therefore, it is not possible to draw more than one parallel line through the given point.

Conclusion:
Based on the above proof, we can conclude that only one parallel line can be drawn passing through a point not on the given line. Therefore, the correct answer is option 'B' - 1.