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

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

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29 Nov 2015, 10:47
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25% (medium)

Question Stats:

70% (01:05) correct 30% (01:20) wrong based on 182 sessions

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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

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

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29 Nov 2015, 11:02
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

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

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30 Nov 2015, 15:12
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

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

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01 Jan 2018, 11:49
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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Re: Which of the following equations represents a line that is perpendicul  [#permalink]

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23 Apr 2018, 05:44
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

Two lines are perpendicular when their slopes are negative reciprocal of each other.

Slope of given line =$$\frac{1}{2}$$

Required slope = $$-2$$

Only equation of line $$3y+6x=12$$ satisfies

$$y = -2x + 12$$

(C)

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Re: Which of the following equations represents a line that is perpendicul   [#permalink] 23 Apr 2018, 05:44
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