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If line \(L\) passes through the points \((\frac{a}{2}, b)\) and \((a, -2b)\), which of the following represents the slope of line \(L\)?
A. \(-\frac{a}{6b}\)
B. \(-{b}{a}\)
C. \(-6\frac{b}{a}\)
D. \(3\frac{a}{2b}\)
E. \(\frac{a}{b}\)
A. \(-\frac{a}{6b}\)
B. \(-{b}{a}\)
C. \(-6\frac{b}{a}\)
D. \(3\frac{a}{2b}\)
E. \(\frac{a}{b}\)
16 Sep 2014, 00:45
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Official Solution:
If line \(L\) passes through the points \((\frac{a}{2}, b)\) and \((a, -2b)\), which of the following represents the slope of line \(L\)?
A. \(-\frac{a}{6b}\)
B. \(-{b}{a}\)
C. \(-6\frac{b}{a}\)
D. \(3\frac{a}{2b}\)
E. \(\frac{a}{b}\)
The slope of the line \(= \frac{\text{(difference in Ys)}}{\text{(difference in Xs)}} = \frac{(-2b - b)}{(a - \frac{a}{2})} = \frac{-3b}{(\frac{a}{2})} = -6(\frac{b}{a})\).
If working with variables presents discomfort for you, you can always plug numbers instead to make the solution easier to grasp. For example, \(a\) could equal 2 or 4 (which needs to be divisible by 2), and \(b\) can be any integer. The downside of this approach is that you will have to plug numbers into each of the answer choices, which takes time. Therefore, using variables is the recommended approach, but both methods work.
Note that while Geometry is not tested on GMAT Focus, coordinate geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.
Answer: C
If line \(L\) passes through the points \((\frac{a}{2}, b)\) and \((a, -2b)\), which of the following represents the slope of line \(L\)?
A. \(-\frac{a}{6b}\)
B. \(-{b}{a}\)
C. \(-6\frac{b}{a}\)
D. \(3\frac{a}{2b}\)
E. \(\frac{a}{b}\)
The slope of the line \(= \frac{\text{(difference in Ys)}}{\text{(difference in Xs)}} = \frac{(-2b - b)}{(a - \frac{a}{2})} = \frac{-3b}{(\frac{a}{2})} = -6(\frac{b}{a})\).
If working with variables presents discomfort for you, you can always plug numbers instead to make the solution easier to grasp. For example, \(a\) could equal 2 or 4 (which needs to be divisible by 2), and \(b\) can be any integer. The downside of this approach is that you will have to plug numbers into each of the answer choices, which takes time. Therefore, using variables is the recommended approach, but both methods work.
Note that while Geometry is not tested on GMAT Focus, coordinate geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.
Answer: C
RenanBragion
11 Jun 2020, 05:16
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I think this is a high-quality question and I agree with explanation.
