BTGmoderatorLU wrote:In the xy-plane, the line k passes through the origin and through the point (a, b), where ab does not equal 0. Is b positive?

(1) The slope of the line is negative.
(2) a < b.

The OA is C.

Can the question be done in the following way?

The equation of the line is y=mx+c.
We are told that it passes through the origin (0,0).
So, the equation of line becomes y=mx.
Find if x is positive.

statement 1: m is negative. x could be positive or negative. insufficient
statement 2: a<b that means x is less than y. insufficient

both :
y=mx
m is negative
so, y=-mx
statement 2 says x,y, so we can see that if x is +ve then y is negative and when x is negative then y is positive. if x has to be less than y, then it has to be positive.

Someone help, please? Thanks!

Given: In the xy-plane, the line k passes through the origin and through the point (a, b), where ab ≠ 0.

To find out: Is b positive?

Let's take each statement one by one.

(1) The slope of the line is negative.

=> The line passes through the quadrant II and IV.

If point (a, b) lies in quadrant II, the answer is Yes, else no since in quadrant IV, b < 0.

(2) a < b.

The point can lie in any quadrant. With a < b, b can still be either positive or negative. Insufficient.

(1) and (2) together

From (1), we know that the point lies wither in quadrant II or in quadrant IV. From (2), we know that a < b, the point can lie only in quadrant II; thus, b is positive, not negative. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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