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# Which of the following equations represents a line perpendicular to li

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Which of the following equations represents a line perpendicular to li  [#permalink]

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04 Jun 2015, 04:08
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66% (01:21) correct 34% (01:35) wrong based on 334 sessions

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Which of the following equations represents a line perpendicular to line k in the figure above?

(A) 3y + 2x = –12
(B) 2y + x = 0
(C) 2y – x = 0
(D) y + 2x = 12
(E) y – 2x = 12

Attachment:

2015-06-04_1507.png [ 19.63 KiB | Viewed 3890 times ]

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Re: Which of the following equations represents a line perpendicular to li  [#permalink]

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04 Jun 2015, 04:24
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Slope of line k is (y2-y1)/ (x2-x1)

= 0- (-6)/ 12-0 = 1/2

Slope of the line perpendicular to line k will have slope of -2 (For perpendicular lines slopes are negative reciprocal of each other)
Only option D has a slope of -2.

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Re: Which of the following equations represents a line perpendicular to li  [#permalink]

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08 Jun 2015, 04:51
Bunuel wrote:

Which of the following equations represents a line perpendicular to line k in the figure above?

(A) 3y + 2x = –12
(B) 2y + x = 0
(C) 2y – x = 0
(D) y + 2x = 12
(E) y – 2x = 12

Attachment:
The attachment 2015-06-04_1507.png is no longer available

MANHATTAN GMAT OFFICIAL SOLUTION:

The product of the slopes of two perpendicular lines is –1. The slope of line k is given by:
$$\frac{rise}{run}=\frac{change \ in \ y}{change \ in \ x}=\frac{0-(-6)}{12-0}=\frac{1}{2}$$.

Thus, the slope of the line perpendicular to k is –2.

Put each choice in slope-intercept form: y = mx + b form, where the slope is m.
Attachment:

2015-06-08_1549.png [ 84.62 KiB | Viewed 3341 times ]
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Re: Which of the following equations represents a line perpendicular to li  [#permalink]

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04 Apr 2017, 16:12
Bunuel wrote:

Which of the following equations represents a line perpendicular to line k in the figure above?

(A) 3y + 2x = –12
(B) 2y + x = 0
(C) 2y – x = 0
(D) y + 2x = 12
(E) y – 2x = 12

Let’s determine the slope for line k. We see that points (12,0) and (0, -6) are on line k.

slope = change in y/change in x

slope = (-6 - 0)/(0 - 12) = -6/-12 = 1/2

The line that is perpendicular to k will have a slope of -2.

Scanning our answer choices, we see that answer choice D is correct because we can manipulate that equation to read y = -2x + 12.

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Re: Which of the following equations represents a line perpendicular to li  [#permalink]

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05 Apr 2017, 03:42
2 Lines will be Perpendicular if the Slopes of both results as -1

For example : m1*m2 = -1

Step 1: Find the slope from the given stem
Step 2 : Find the slope from the answer Choices

If Slopes give -1 . then that is the answer.

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Re: Which of the following equations represents a line perpendicular to li  [#permalink]

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05 Apr 2017, 07:09
D.
Y= (1/2)x-6 is the equation of the line K. Now line perpendicular to this line should have -2 (m1*m2= -1) as the coefficient of x. Hence option D

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Re: Which of the following equations represents a line perpendicular to li  [#permalink]

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13 Sep 2018, 23:38
Slope of the line perpendicular to line k will have slope of -2
(For perpendicular lines slopes are negative reciprocal of each other)

ax+by+c = 0; where -a/b is slope.
So the calculated slope of option should be -2.
A) 3y + 2x = –12 : 2/3 Incorrect
(B) 2y + x = 0 : 1/2 Incorrect
(C) 2y – x = 0 : -1/2 Incorrect
(D) y + 2x = 12 : 2 correct, as slope is -a/b; so -1*2/1
(E) y – 2x = 12 : -2/1 Incorrect
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Re: Which of the following equations represents a line perpendicular to li  [#permalink]

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16 Jan 2019, 12:30
Hi All,

We're asked which of the 5 answers is the equation for a line that is perpendicular to line K in the figure above. This question is based on line/graphing rules.

To start, a PERPENDICULAR line is one that has an "opposite inverse" slope (sometime called a "negative reciprocal" slope). For example, if we start with a line that has a slope of 3, then a perpendicular line to that line would have a slope of -1/3.

Here, we can determine the slope of the given line... (change in Ys)/(change in Xs) = (-6 - 0)/(0 - 12) = -6/-12 = +1/2

Since the given line has a slope of +1/2, we know that the perpendicular line will have a slope of -2/1 = -2.

At this point, it would help to convert the answer choices into "slope intercept" format --> re: Y = (M)(X) + B. We need a line that begins with Y = -2X...... It shouldn't take too much work to find the one answer that fits that pattern...

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Re: Which of the following equations represents a line perpendicular to li   [#permalink] 16 Jan 2019, 12:30
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