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In the xy-plane, line l and line k intersect at the point

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In the xy-plane, line l and line k intersect at the point [#permalink] New post 26 Sep 2010, 10:49
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In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?

(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.
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Re: Slope of Line [#permalink] New post 26 Sep 2010, 11:19
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udaymathapati wrote:
In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?
(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.



Line l passes through the point (16/5, 12/5). If we knew some other point through which line l passes then we would be able to calculate the slope: the slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.

(1) The product of the slopes of line l and line k is -1 --> line l and k are perpendicular to each other (the two lines are perpendicular if and only the product of their slopes is -1). Not, sufficient, as we can have infinite # of perpendicular lines passing through some point (16/5, 12/5).

(2) Line k passes through the origin --> we have the second point for line k, so we can calculate the slope of k, but we don't know the relationship between the lines l and k. Not sufficient.

(1)+(2) We can calculate the slope of k and we know that the product of the slopes of l and k is -1, so we can calculate the slope of line l too. Sufficient.

Answer: C.

For more on these issues check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.
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Re: Slope of Line [#permalink] New post 26 Sep 2010, 11:22
We know one point in the coordinate system.

(1) Insufficient. First, you must know that perpendicular lines have negative reciprocal slopes. We know that the product of the slopes of l and k is -1, therefore they are perpendicular.

(2) Insufficient. We can now solve for the slope of k, but we know nothing about l.

(1+2) Sufficient, Since we know the slope of k, then we know the slope of l is -1/k.
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Re: Slope of Line [#permalink] New post 26 Sep 2010, 11:24
Bunuel, you are too quick!
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Re: Slope of Line [#permalink] New post 14 Oct 2010, 18:34
C

1) says l and k have opposite slopes. so given point is perpendicular point on intersection ==> NOT SUFF though to find the slope

2) point of intersection and origin will give us the slope of k ==> NOT SUFF by itself since we would not know about the perpendicular bisection

1 + 2 ==> -1/slope of k == slope of l ==> SUFF
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Re: In the xy-plane, line l and line k intersect at the point [#permalink] New post 15 Oct 2013, 23:38
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Re: In the xy-plane, line l and line k intersect at the point   [#permalink] 15 Oct 2013, 23:38
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