Question

choose the origin on a straight line the quantities measured to right are taken positive and these measured to the left are taken as negative

Answer 1

If you are asking WHY that's the way it is, well, say it's plain old convention. You could do it the other way around. You can do whatever you please with any axis you want, but that will change the variables an equations you use to do the math later on. they have been derived in accordance with the convention that right and left is +x and -x. up and down is +y and -y, and forward and backward is -z and +z (that's a point which is arguable. Consider the corner of a room and compare it with the axes. now take the corner on the adjacent side and the z orientation reverses) so you will have to make adjustments to the formulae to get things right. this is true even for a line which is NOT an axis, say a line passing through the origin(like you have mentioned in the question).

If your question was something ELSE because it is a little confusing, let me know in the comments and i will try to answer it.