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

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alltimeacheiver
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In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0 [#permalink] New post  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
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Re: In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0 [#permalink] New post  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.

Answer: A.

For more on this topic check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html
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Ultimor
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Re: In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0 [#permalink] New post  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, where abc 0 [#permalink] New post  09 Apr 2022, 14:52
Hi brunel, for statement 2, can we not use −c/b and why ? Thanks
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Re: In the xy-plane, the line with equation ax + by + c = 0, where abc 0 [#permalink] New post  13 May 2023, 01:18
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Re: In the xy-plane, the line with equation ax + by + c = 0, where abc 0 [#permalink]
13 May 2023, 01:18
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