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Slopes

by heshamelaziry » Wed Nov 04, 2009 9:25 am
Q. The product of slopes of two lines L1 and L2 is -1. If the lines intersect at point (2,-2) and the x intercept of line L1 is 8, what is the y intercept of line L2?

A) 12
B) -12
C) 8/3
D) -8/3
E) None of the above

[spoiler]OA is E. I got as far as getting the slope of L1 and L2 but don't know how to proceed ?[/spoiler]
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Re: Slopes

by Stuart@KaplanGMAT » Wed Nov 04, 2009 9:39 am
heshamelaziry wrote:Q. The product of slopes of two lines L1 and L2 is -1. If the lines intersect at point (2,-2) and the x intercept of line L1 is 8, what is the y intercept of line L2?

A) 12
B) -12
C) 8/3
D) -8/3
E) None of the above
If the product of two slopes is -1, then they are perpendicular and their slopes are negative reciprocals of one another.

Since the x-intercept of L1 is 8, we can find its slope using the point we're given.

We know that (8,0) and (2,-2) are both on L1, so:

slope = rise/run = change in y/change in x
= (0 - (-2))/(8 - 2) = 2/6 = 1/3

Accordingly, the slope of L2 is -1/(1/3) = -3

Now we have the slope of L2 and a point on the line, so we can find the equation of the line.

y = mx + b

in which m=slope and b=y-int

Plugging in:

m = -3
x = 2
y = -2

-2 = -3(2) + b
-2 = -6 + b
4 = b

4 isn't one of the first four choices, so choose E.
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