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
line k in xy-plane
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Hi there!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
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!
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