Question

Is it possible for a line to pass through only one quadrant? How about four quadrants? explain

Answer 1

Yes it is possible for a line to only start in one quadrant and never leave that quadrant and vice versa a line can start in one quadrant and pass into another quadrant but how will you know if you line will be in certain or multiple quadrants simple just look at your points given if you have the points (3,4) (4,5) you notice that your X's are positive and your Y's are positive there is only one quadrant were your X and Y are positive and that is quadrant 1 but lets say you have points (-4,5),(3,4) you see how one of the points have a negative X and a positive Y there is only one quadrant that has a negative X and a positive Y that is quadrant 2 and and for point (3,4) that is in quadrant 1 so your line will run through quadrant 2 and 1 

yes it is possible for a line to only be in one quadrant and it is also possible for a line to be in multiple quadrants basically it can be any place on a plane  
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Answer 2

It is not possible for a line to pass through one quadrant. A line is a 2 dimensional shape and crosses through 2 quadrants, even if passing through the origin. If a line passes through the origin, it still only enters and exits 2 quadrants. there must be a curvature in order to cross 4 quadrants.