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

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In the xy-plane, the line with equation ax + by + c = 0, [#permalink] New post 11 Feb 2011, 02:22
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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
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Re: co-ordinate geomatry [#permalink] New post 11 Feb 2011, 03:50
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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.

Answer: A.

For more on this topic check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html
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Re: co-ordinate geomatry [#permalink] New post 19 May 2011, 01:37
a gives value of b.

b gives a ratio.

A sufficient.
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Coordinate Geometry [#permalink] New post 11 Feb 2013, 08:32
In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0, has slope 3/2. What is the value of b?
(1) a = 4
(2) c = −6
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Can someone please solve and explain the problem to me???
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In the xy-plane, the line with equation ax+by+c=0, where abc [#permalink] New post 29 Apr 2013, 01:43
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

I don't fully understand the Official explanation. I would appreciate if someone could explain it a bit more. Thanks!
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Re: In the xy-plane, the line with equation ax+by+c=0, where abc [#permalink] New post 29 Apr 2013, 01:49
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Stiv 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

I don't fully understand the Official explanation. I would appreciate if someone could explain it a bit more. Thanks!


Merging similar topics. Please refer to the solution above.
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Re: co-ordinate geomatry [#permalink] New post 29 Apr 2013, 02:40
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Bunuel wrote:

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



should'nt it be that way:

\(ax + by + c = 0\) --> \(y=-\frac{a}{b}*x-\frac{c}{b}\).
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Re: co-ordinate geomatry [#permalink] New post 29 Apr 2013, 02:42
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Ultimor wrote:
Bunuel wrote:

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



should'nt it be that way:

\(ax + by + c = 0\) --> \(y=-\frac{a}{b}*x-\frac{c}{b}\).


Typo edited. Thank you. +1.
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COLLECTION OF QUESTIONS:
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Re: In the xy-plane, the line with equation ax + by + c = 0, [#permalink] New post 29 Apr 2013, 02:47
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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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In the xy-plane, the line with equation ax+by+c=0, where abc [#permalink] New post 06 May 2013, 02:03
In the xy-plane, the line with equation ax+by+c=0, where \(abc\neq{0}\), has slope 2/3. What is the value of b?
1) a=4
2) c= -6
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Re: In the xy-plane, the line with equation ax+by+c=0, where abc [#permalink] New post 06 May 2013, 02:14
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Re: In the xy-plane, the line with equation ax + by + c = 0, [#permalink] New post 23 Jun 2015, 12:11
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Re: In the xy-plane, the line with equation ax + by + c = 0,   [#permalink] 23 Jun 2015, 12:11
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