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# Which of the following lines is perpendicular to y = − 2x + 3 and has

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Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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29 Dec 2015, 07:59
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71% (00:52) correct 29% (01:11) wrong based on 304 sessions

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Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 3?

A. y = -1/2*x + 3
B. y = 1/2*x - 3
C. y = 1/2*x + 3
D. y = 2x + 3
E. y = 2x − 3

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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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29 Dec 2015, 08:51
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Slope of y = − 2x + 3 is -2.
Product of slope of Perpendicular lines is always -1. Therefor slope of a line perpendicular to the above line is 1/2
1/2*-2 = -1
General equation of a line perpendicular to y = − 2x + 3 is y = 1/2x + k where is the k is the y intercept.

y-intercept of y = 2x − 3 is -3

Therefore equation of the required line is
y = 1/2 x - 3
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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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29 Dec 2015, 11:01
Since our line has to perpendicular to y = − 2x + 3
Slope of this line , m = -2
Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)

y-intercept of line L is same as y intercept of line y = 2x − 3
y - intercept of line L = -3
Required line = 1/2* x - 3

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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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01 Jan 2016, 12:41
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Hi All,

This question is based on a pair of graphing/line rules that you might not actually use on Test Day (but they're good to know since they're part of the broader group of line rules that come with Co-ordinate Geometry).

We're asked which of the following lines is PERPENDICULAR to y = − 2x + 3 and has the same Y-INTERCEPT as y = 2x − 3.

The second piece of information is easier to deal with, so we'll start there. Both of the given equations are written in slope-intercept 'format', which is helpful:

Slope-intercept: Y = MX + B, where M is the slope and B is the Y-intercept of the line.

Since the second equation has a y-intercept of -3, the line we're looking for ALSO has a y-intercept of -3.
Eliminate Answers A, C and D.

Perpendicular lines criss-cross one another and form 90 degree angles. The lines have "opposite inverse" slopes (sometimes called "negative reciprocal" slopes). The line that we're given has a slope of -2, so the "opposite inverse" line would have a slope of +1/2.

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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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01 Jan 2016, 20:37
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Bunuel wrote:
Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 3?

A. y = -1/2*x + 3
B. y = 1/2*x - 3
C. y = 1/2*x + 3
D. y = 2x + 3
E. y = 2x − 3

This question tests your knowledge about the various terms used in coordinate geometry.

If two lines are perpendicular, then the product of their slopes will be = -1

How to find the slope:
Any line can be written in the form y = mx + c
Where m is the slope and c is the intercept.

In this case, slope of y = -2x + 3 is "-2"

Hence the answer choice should have the slope as "1/2"
Only options B and C remain.

Next we need the intercept to be same.
The intercept given is "-3"
Hence the equation of the line will be y = 1/2*x - 3

Option B
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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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10 Mar 2017, 10:32
Bunuel wrote:
Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 3?

A. y = -1/2*x + 3
B. y = 1/2*x - 3
C. y = 1/2*x + 3
D. y = 2x + 3
E. y = 2x − 3

Recall that the slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the value of its y-intercept. We see that the line y = -2x + 3 has a slope of -2 and the line y = 2x - 3 has a y-intercept of -3.

Since the slopes of perpendicular lines are negative reciprocals of each other, the slope of the line that is perpendicular to a line with slope of -2 is 1/2. We also see that the line needs to have a y-intercept of 3; thus, the equation of that line is:

y = (1/2)x - 3

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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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30 Jun 2017, 15:04
Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 3?

Two lines are said to be parallel if the multiplication of their slope is $$= -1$$

Given Line has a Slope = -2

Hence, we are looking for slope of $$\frac{1}{2}$$ as $$\frac{1}{2} * -2 = -1$$

And y intercept of the second like = -1

Hence, Line with Slope $$\frac{1}{2}$$ and Y Intercept $$= -3$$ is line B

$$y = \frac{1}{2}*x - 3$$

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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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26 Jul 2017, 23:32
For this question i went through the options. The slope of a line is -2 and the slope of the perpendicular line is 1/2 because the product of the 2 slopes must be -1(-2*1/2). So the options B and C only can be considered. Now since the y intercept must be (0,-3) only option B must be considered. Am i correct in my concept . Kindly help. Thanks
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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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26 Jul 2017, 23:39
Bunuel wrote:
Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 3?

A. y = -1/2*x + 3
B. y = 1/2*x - 3
C. y = 1/2*x + 3
D. y = 2x + 3
E. y = 2x − 3

Slope of y = -2x+3 is -2
slope of line perpendicular to this line = 1/2
Line perpendicular to y = -2x+3 is y = 1/2*x + m where is m is intercept on y -axis

y-intercept of y = 2x -3 is -3

So, the desired equation becomes y = 1/2*x -3

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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has  [#permalink]

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25 Nov 2018, 06:24
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Re: Which of the following lines is perpendicular to y = − 2x + 3 and has   [#permalink] 25 Nov 2018, 06:24
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