This was a true or false question with the answer being false.
In what case would a line equation, where for every (x,y) there needs to be
(-x,-y) as a solution does not pass through the origin?
In what case would a line equation, where for every (x,y) there needs to be
(-x,-y) as a solution does not pass through the origin?
There are edge cases where a graph is symmetrical about the origin while not containing the origin itself; take for instance y=1/x
(0, 0) is not in the domain of points satisfied by the equation; however, the graph is still an odd function. That is just one case that proves that the answer will be false.
If the question was denoting a straight line or a line with a complete domain, then the answer, to my knowledge, would be true. But given the presence of the edge case denoted above as well as others (see if you can come up with a few), the correct answer is false.
Yeah, I guess I did not consider equations like y=1/x as line equations as we can also consider hyperbola, ellipse and circle equations that can be symmetrical about origin but not pass through origin. But I would classify them as conic sections not lines. Thanks for the clarification, that clears up where my mind did not go to.