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

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Intern
Joined: 09 Feb 2011
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In the xy-plane, the line with equation ax + by + c = 0, [#permalink]

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11 Feb 2011, 03:22
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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
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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11 Feb 2011, 04:50
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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?

$$ax + by + c = 0$$ --> $$y=-\frac{a}{b}*x-\frac{c}{b}$$. So the slope equals to $$-\frac{a}{b}=\frac{2}{3}$$.

(1) a = 4 --> we can find $$b$$ form $$-\frac{a}{b}=\frac{2}{3}$$. Sufficient.
(2) c = -6 --> we cannot find $$b$$ from $$-\frac{a}{b}=\frac{2}{3}$$. Not sufficient.

For more on this topic check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html
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Intern
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Location: Germany
Concentration: Finance, Accounting
GMAT Date: 05-28-2013
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Re: In the xy-plane, the line with equation ax + by + c = 0, [#permalink]

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29 Apr 2013, 03:47
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Further, the explanation as requested:

There are 2 popular forms of writing an equation. The forms are:

(I) 0 = a*x + b*y +c and

(II) y = m*x + n

These equations can be transofmred easiliy into each other. When you do that you will find that m= -(a/ b) and n= -(c/b).

In the form (II) m can be understood as the slope of the line. That is why we can take from the problem statement that m = -(a/b) = 2/3

Rest should be clear.
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Re: In the xy-plane, the line with equation ax + by + c = 0, [#permalink]

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06 Oct 2017, 05:14
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the xy-plane, the line with equation ax + by + c = 0,   [#permalink] 06 Oct 2017, 05:14
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