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In the xy-coordinate plane, line l and line k intersect

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by varun289 » Thu Dec 13, 2012 11:39 am
210. 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.
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Source: — Problem Solving |

by puneetkhurana2000 » Thu Dec 13, 2012 12:03 pm
K=a1x+b1
L=a2x+b2
Is a1a2 < 0 ?

Statement 1)

(-b1/a1) x (- b2/a2) > 0 or b1b2/a1a2 > 0

We don't know if both are either positive or negative, so Not Sufficient!!!

Statement 2)

b1b2 < 0

No Information about a1a2, so Not Sufficient!!!

Together

b1b2/a1a2 > 0
b1b2 < 0

Hence, a1a2 < 0

Answer C

Note: - The information that they intersect at (4,3) is irrelevant unless you solve this by drawing some lines. If algebra to be used, we don't need this information as explained above.

Hope this helps!!!
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