Question

In the xy-plane, the line k passes through the origin and through the point (a,b), where ab ≠ 0. Is b positive? (1) The slope of line k is negative. (2) a < b

Answer 1

Yes

Explanation:

Since the line passes through the origin, when calculating the slope of the line, we can make use of the origin as a point. So pests say (x1, y1) = (0,0) and (x2,y2) is (a,b). Hence the slope is b/a.

Now we now act on this information to solve the problem. Firstly, we know that the slope is negative, this means either a or b is negative but both are not negative. Secondly, b is greater than a. This mean b is the positive term as both terms cannot be negative.