One thing people miss about this question is that a line stretches infinitely in both directions - if a question wanted to limit the line, it would use the term "line segment".btgyes wrote:In the rectangular coordinate system, line k has equation y = mx + b, where m and b are constants. does the line k intersect quadrant II?
1) Slope of k is -1/6
2) The y-intercept of k is -6
With this in mind, all you really need to know is whether the line will pass through quadrant II (negative x, positive y quadrant) at SOME point.
(1) As long as the line has a negative slope (doesn't matter if it's a negative fraction or negative number smaller than -1), the line will pass through quadrant II somewhere - the line declines from left to right (think of a car driving on the line from left to right - with a negative slope, that car is driving downhill), so at some point the line will ht Quad II.
You need the y intercept (in stat. (2) to determine whether that point of intersection with quad II will happen left or right of the y-axis, but not that the intersection will happen. Thu, stat. (1) is sufficient to answer the question on its own.
(2) alone, this is insufficiient, since you do not know the slope.
If the slope of the line is negative, then the line will hit the second quadrant somewhere to the left of the y axis.\
If the slope of the line is positive, or zero (parallel to the x axis), the the line will never hit the second quad.
Thus, (2) is insufficient. Answer is A.
