In the xy-coordinate plane, line l and line k intersect at the point (4,3). Is the product of their slopes negative?
(1) The product of the x-intercepts of lines l and K is positive.
(2) The product of the y-intercepts of lines l and k is negative.
Another coordinate geometry question
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Hi,
Let line l be y = ax+b, where slope is a and y-intercept is b
and line k be y = cx+d where slope is c and y-intercept is d
Product of slopes is a.c
From(1):
X-intercept of l is (-b/a)
X-intercept of k is (-d/c)
Product is bd/ac > 0
Not sufficient
From(2):
Product of y-intercepts is b.d<0
Not sufficient
Both (1)&(2): bd/ac> 0 and bd<0. So ac must be negative
Sufficient
Hence, C
Let line l be y = ax+b, where slope is a and y-intercept is b
and line k be y = cx+d where slope is c and y-intercept is d
Product of slopes is a.c
From(1):
X-intercept of l is (-b/a)
X-intercept of k is (-d/c)
Product is bd/ac > 0
Not sufficient
From(2):
Product of y-intercepts is b.d<0
Not sufficient
Both (1)&(2): bd/ac> 0 and bd<0. So ac must be negative
Sufficient
Hence, C
Cheers!
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Things are not what they appear to be... nor are they otherwise
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Think of the possibilities for 2 lines intersecting.
They could both be the same vertical line. They could both be the same horizontal line. They could both tilt to the right (positive slopes). They could both tilt to the left (negative slopes). Or one could tilt to the right and the other could tilt to the left.
To know what the product of the slopes will be, we need to get a better sense of how these lines appear on the graph.
(1) If the product is positive, this could mean that both x-intercepts are positive, or both are negative. This is not enough information to determine the slope.
(2) If the product is negative, this means that one y-intercept is negative, and the other is positive. Again, this is not enough information.
If we combine however, we have enough. Both lines will have to have positive x-intercepts for one of them to have a negative y-intercept. They will cross each other like a "X" at (4,3), and the slopes will have opposite signs.
IMO: C
They could both be the same vertical line. They could both be the same horizontal line. They could both tilt to the right (positive slopes). They could both tilt to the left (negative slopes). Or one could tilt to the right and the other could tilt to the left.
To know what the product of the slopes will be, we need to get a better sense of how these lines appear on the graph.
(1) If the product is positive, this could mean that both x-intercepts are positive, or both are negative. This is not enough information to determine the slope.
(2) If the product is negative, this means that one y-intercept is negative, and the other is positive. Again, this is not enough information.
If we combine however, we have enough. Both lines will have to have positive x-intercepts for one of them to have a negative y-intercept. They will cross each other like a "X" at (4,3), and the slopes will have opposite signs.
IMO: C
Vivian Kerr
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It's not necessary.
Vivian Kerr
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Thank you for all the "thanks" and "follows"!
GMAT Rockstar, Tutor
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https://www.yelp.com/biz/gmat-rockstar-los-angeles
Former Kaplan and Grockit instructor, freelance GMAT content creator, now offering affordable, effective, Skype-tutoring for the GMAT at $150/hr. Contact: [email protected]
Thank you for all the "thanks" and "follows"!