Topic moved to DS subforum.kenguva wrote:
If the slopes of the line l1 and l2 are of the same sign, is the slope of the line l1 greater than that of line l2?
(1) Lines l1 and l2 intersect at point(a,b) where a and b are positive
(2) The X-intercept of line l1 is greater than the X-intercept of line l2
If the slopes of the line l1 and l2 are of the same sign, is the slope of the line l1 greater than that of line l2?(1) Lines l1 and l2 intersect at point (a,b) where a and b are positive --> clearly insufficient: we can rotate the lines on this point so that we get an YES, as well as NO answers. Not sufficient.
(2) The X-intercept of line l1 is greater than the X-intercept of line l2 --> also insufficient: we can draw numerous lines with the same sign slopes so that we get an YES, as well as NO answers. Not sufficient.
(1)+(2) We know that: the slopes of the lines are of the same sign, that they intersect in I quadrant and the X-intercept of line l1 is greater than the X-intercept of line l2. There can be two cases:
Attachment:
graph 5.png [ 19.87 KiB | Viewed 1288 times ]
You can see that in both cases the slope of L1 is greater than the slope of L1 as
a steeper incline indicates a higher absolute value of the slope.
In red case: both lines have positive slope, L1 is steeper thus its slope is greater than the slope of L2;
In blue case: both lines have negative slope, L2 is steeper thus its slope is
more negative (the absolute value of its slope is greater) than the slope of L1, which also means that the slope of L1 is greater than the slope of L2.
Answer: C.
For more on this topic check Coordinate Geometry chapter of Math Book:
math-coordinate-geometry-87652.htmlP.S.
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51% (02:56) correct
