josh80 wrote:In the xy-plane, the line k passes through the origin and through points (a,b), where ab is not equal to 0. Is b positive?

1) the slope of line k is negative

2) a < b

OA C

Hi there!

We know that line K passes through the origin, so it must pass through exactly 2 of the 4 quadrants (ab isn't 0, so we know that line K isn't just one of the axes).

Q: is b positive? We need info about which quadrant point a,b is in.

(1) the slope is negative.

If the slope is negative, we know we go from top left to bottom right - i.e. the line passes through the 2nd and 4th quadrants. Well, top left is (-,+) and bottom right is (+,-). Is (b) positive? If we're in top left, sure. If we're in bottom right, nope!

Therefore, (1) is insufficient... eliminate A and D.

(2) a < b

nothing at all about sign - insufficient... eliminate B.

Together: we know we have either (-,+) or (+,-). Since a<b, we have to be in the (-,+) quadrant, which means that b MUST be positive.

Together sufficient... choose C!