Question

What allows me to draw an extra line that is parallel to another line

Answer 1

Parallel lines have the same slope and different y-intercept as the original equation.

Answer 2

sorry i was looking for in geometry what would be the logical reason that allows me to draw an extra line. Like a theorem or postulate

Answer 3

My teacher makes us use the "draw line step". Ex. Draw line AB parallel to line BC. The reason is the theorem/postulate that allows you to draw that line with certainty, in the case I mentioned above it would be: Through a point not on a line, there is exactly one line parallel to the original line.