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Which of the following equations represents a line that is perpendicul

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Which of the following equations represents a line that is perpendicul [#permalink]

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Which of the following equations represents a line that is perpendicular to y=1/2*x+2?

A. y−2x=8
B. 2x+4y=10
C. 3y+6x=12
D. 4y−8x=16
E. 5x−10y=20
[Reveal] Spoiler: OA

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Re: Which of the following equations represents a line that is perpendicul [#permalink]

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New post 29 Nov 2015, 10:02
For two lines to be perpendicular, the product of slopes should be equal to -1.

Slope of line 1 = 1/2

Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2

Answer: C

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Re: Which of the following equations represents a line that is perpendicul [#permalink]

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New post 30 Nov 2015, 14:12
Hi All,

This question asks for a line that is perpendicular to the line Y = (1/2)(X) + 2.

When graphing lines, it's often easiest for most Test Takers to put the line in slope-intercept 'format' (the same format as the one used in the given equation above). Perpendicular lines have slopes that are 'opposite inverse' (sometimes called 'negative reciprocal'), so we're looking for a line that has a slope of -2 (since the opposite of a positive is a negative and the inverse of 1/2 is 2).

Rather than convert all 5 answer choices to slope-intercept format, we can use some patterns to our advantage. To start, the slope will have to be NEGATIVE. Eliminate Answers A and D (their slopes will be positive). With the remaining 3 answers, we have:

B: Y = (1/2)X + 5/2
C: Y = -2X + 4
E: Y = (-1/2)X -2

Final Answer:
[Reveal] Spoiler:
C


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Re: Which of the following equations represents a line that is perpendicul [#permalink]

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New post 01 Jan 2018, 10:49
Bunuel wrote:
Which of the following equations represents a line that is perpendicular to y=1/2*x+2?

A. y−2x=8
B. 2x+4y=10
C. 3y+6x=12
D. 4y−8x=16
E. 5x−10y=20


VERITAS PREP OFFICIAL SOLUTION:

In order for two lines to be perpendicular, the slopes need to be negative reciprocals of each other. Since the given slope is 1/2, you're looking for a slope of −2.

To find the slope, you need to put the equations in point-slope form, y = mx + b, where m is the slope. Checking the answer choices quickly:

Choices A, D, and E will each give x a positive coefficient, as your first step is to get y on the opposite side of the equation from x.

Only choice C simplifies to a coefficient of −2:

3y + 6x = 12

3y = −6x + 12

y = −2x + 4

So C is the correct answer.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Kudos [?]: 139367 [0], given: 12787

Re: Which of the following equations represents a line that is perpendicul   [#permalink] 01 Jan 2018, 10:49
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