In the xy-coordinate plane, , line l and line k intersect at : DS Archive
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# In the xy-coordinate plane, , line l and line k intersect at

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In the xy-coordinate plane, , line l and line k intersect at [#permalink]

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22 Apr 2006, 08:27
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In the xy-coordinate plane, , line l and line k intersect at point (4,3). Is the product of their slopes negative?

1) The product of the x-intercepts of the lines l & K is positive.
2) The product of the y-intercepts of the lines l & K is negative.
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22 Apr 2006, 10:09
Equation of line in Intercept form x/a + y/b = 1 where x intercept is a and y intercept is b. Slope of the line is -b/a.

Let the two lines in this form be x/a1 + y/b1 = 1 and x/a2 + y/b2 = 1.

Then the product of the slopes is -(b1/a1) * -(b2/a2) = b1*b2/a1*a2

First condition gives a1*a2>0
2nd one gives b1*b2 <0

Hence together are necessary to conclude b1*b2/a1*a2 <0

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22 Apr 2006, 10:22
OA is C. Thanks.

The information about Point (4,3) seems redundant.
22 Apr 2006, 10:22
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