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# In the xy-plane, the line with equation ax + by + c = 0,

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Senior Manager
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In the xy-plane, the line with equation ax + by + c = 0, [#permalink]

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02 Jul 2009, 07:25
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In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0, has slope 2/3 . What is the value of b?
(1) a = 4
(2) c = −6

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02 Jul 2009, 10:08
Vavali wrote:
In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0, has slope 2/3 . What is the value of b?
(1) a = 4
(2) c = −6

Rewrite the equation in standard form (y = mx +b); then m will be the slope:

by = -ax - c
y = (-a/b)x - c/b

So the slope of our line is -a/b, and the y-intercept is -c/b. Now we know that the slope is also equal to 2/3, so:

-a/b = 2/3
b = -3a/2

So with a we can find b, and with c we cannot. The answer is A.
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Senior Manager
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02 Jul 2009, 11:28
First I solve for the standard equation format: y = mx + b

-(a/b)x – c/b = y

1) Plug in the known values
-(4/b)x – c/b = y
If slope = 2/3, then -4/b = 2/3
So b = -6
SUFFICIENT

2) Plug in the known values
-(a/b)x – (-6)/b = y
We still can’t figure out b, so INSUFFICIENT

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03 Jul 2009, 22:13
A

Same expalanion as IanStewart .
Re: xy plane   [#permalink] 03 Jul 2009, 22:13
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