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# Line L has a slope that is greater than -2. Is the

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Line L has a slope that is greater than -2. Is the [#permalink]  20 Jan 2008, 22:03
Line L has a slope that is greater than -2. Is the x-intercept of line L negative?

1.L passes through the point (3,-7)
2.L passes through the point (5,-9)
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Re: coordinate geometry [#permalink]  20 Jan 2008, 23:11
Expert's post
A

we can solve it by drawing or by algebra.

L: $$y=ax+b$$ and a e $$(-2,+\infty)$$
the x-intercept of line L is b

1. $$-7=a*3+b$$ ==> $$b=-3*a-7$$ b e $$(-\infty,-1)$$ suff.

2. $$-9=a*5+b$$ ==> $$b=-5*a-9$$ b e $$(-\infty,1)$$ insuff.
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Last edited by walker on 20 Jan 2008, 23:47, edited 1 time in total.
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Re: coordinate geometry [#permalink]  21 Jan 2008, 02:28
marcodonzelli wrote:
walker wrote:
A

we can solve it by drawing of by algebra.

L: $$y=ax+b$$ and a e $$(-2,+\infty)$$
the x-intercept of line L is b

1. $$-7=a*3+b$$ ==> $$b=-3*a-7$$ b e $$(-\infty,-1)$$ suff.

2. $$-9=a*5+b$$ ==> $$b=-5*a-9$$ b e $$(-\infty,1)$$ insuff.

yep

I think C is correct

x-intercept of L is under control not only of b, but also a.
x= - b/a

1. x = (-3a -7)/a =-3 - 7/a, x-intercept wil (-) if a>0 and will (+) if -2<a<0 --> not sufficient

2. x = - 5 - 9/a --> not sufficient

1 and 2 combined: a = 1, b = - 13, so x - intercept negative --> suff.

C
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Re: coordinate geometry [#permalink]  21 Jan 2008, 03:40
Expert's post
You are right, guys. x-intercept means interception of L with x-axis (I thought with y-axis).
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Re: coordinate geometry [#permalink]  21 Jan 2008, 08:46
marcodonzelli wrote:
Line L has a slope that is greater than -2. Is the x-intercept of line L negative?

1.L passes through the point (3,-7)
2.L passes through the point (5,-9)

Seems to be C.

The line has a slope greater than -2, meaning the slope can be + or -.

Not just visually imagining this, we can see that S1 and S2 are insuff.

Together we have the slope.
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Re: coordinate geometry [#permalink]  11 Feb 2008, 10:07
It should be C.

1: -7=3m+b
b=-7-3m
since we want that b<0, it should be m>-7/3. actually m could be included b/w -2 and -7/3, thus insuff.

2: -9=5m+b
b=-9-5m
following the same reasoning as above we have that m must be>-9/5. thus insuff

let's try c:

b=-7-3m
b=-9-5m

thus m =-1 and b=-4, thus suff
Re: coordinate geometry   [#permalink] 11 Feb 2008, 10:07
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