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# Line C is a straight line in the coordinate geometry plane defined by

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Math Expert
Joined: 02 Sep 2009
Posts: 49320
Line C is a straight line in the coordinate geometry plane defined by  [#permalink]

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06 Jun 2017, 10:31
00:00

Difficulty:

35% (medium)

Question Stats:

64% (00:49) correct 36% (00:51) wrong based on 128 sessions

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Line C is a straight line in the coordinate geometry plane defined by the equation y=ax+b, for which a and b are constants. What is the value of a?

(1) Line C is perpendicular to a line with the equation y=−2x+5
(2) Line C is parallel to a line with the equation y=(1−a)x+b+2

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Re: Line C is a straight line in the coordinate geometry plane defined by  [#permalink]

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06 Jun 2017, 11:10
Bunuel wrote:
Line C is a straight line in the coordinate geometry plane defined by the equation y=ax+b, for which a and b are constants. What is the value of a?

(1) Line C is perpendicular to a line with the equation y=−2x+5
(2) Line C is parallel to a line with the equation y=(1−a)x+b+2

I think the answer should be D.
Statement 1 gives a which is slope as 1/2.
Statement also gives a which is slope as 1/2. a=1-a, so a =1/2
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Re: Line C is a straight line in the coordinate geometry plane defined by  [#permalink]

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08 Jun 2017, 09:16
Bunuel wrote:
Line C is a straight line in the coordinate geometry plane defined by the equation y=ax+b, for which a and b are constants. What is the value of a?

(1) Line C is perpendicular to a line with the equation y=−2x+5
(2) Line C is parallel to a line with the equation y=(1−a)x+b+2

stat 1 : perpendicular lines have slope as m1 * m2 = -1
so slope can be calculated from this..

stat2: parallel line have same slope,,,hence suff

ans D
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Re: Line C is a straight line in the coordinate geometry plane defined by  [#permalink]

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08 Jun 2017, 20:15
Bunuel wrote:
Line C is a straight line in the coordinate geometry plane defined by the equation y=ax+b, for which a and b are constants. What is the value of a?

(1) Line C is perpendicular to a line with the equation y=−2x+5
(2) Line C is parallel to a line with the equation y=(1−a)x+b+2

Question: What is the value of a = What is the slope of line?

Statement 1: Line C is perpendicular to a line with the equation y=−2x+5
Perpendicular lines have relation of slopes as $$m_1*m_2 = -1$$
i.e. a*(-2) = -1
i.e. a = 1/2
SUFFICIENT

Statement 2: Line C is parallel to a line with the equation y=(1−a)x+b+2
Parallel lines have relation of slopes as $$m_1 = m_2$$
i.e. a = (1-a)
i.e. a = 1/2
SUFFICIENT

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Re: Line C is a straight line in the coordinate geometry plane defined by  [#permalink]

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17 Jun 2017, 10:15
Bunuel wrote:
Line C is a straight line in the coordinate geometry plane defined by the equation y=ax+b, for which a and b are constants. What is the value of a?

(1) Line C is perpendicular to a line with the equation y=−2x+5
(2) Line C is parallel to a line with the equation y=(1−a)x+b+2

We can apply simple algebra to solve this question

Statement 1
Because we have the slope of a perpendicular line we of course can know the slope of the other line- just the negative reciprocal

Suff

Statement 2

This line is parallel- the 2 added to the end doesn't really mean anything- ignore it- algebraic the important thing in this question

(1-a)x= ax
1-a=a
1= 2a
a= 1/2

Thus
"D"
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Re: Line C is a straight line in the coordinate geometry plane defined by  [#permalink]

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29 Jun 2018, 00:00
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Re: Line C is a straight line in the coordinate geometry plane defined by &nbs [#permalink] 29 Jun 2018, 00:00
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# Line C is a straight line in the coordinate geometry plane defined by

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