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Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll

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Bunuel
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Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  01 Nov 2019, 04:30
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Line P is described by the equation \(3x + 2y - 4 = 0\). Which of the following lines is parallel to P and has the same x-intercept as the line \(5x - y + 10 = 0\)?


A. \(6x = -4y + 8\)

B. \(-y = (\frac{3}{2})x + 5\)

C. \(3y = (- \frac{9}{2})x - 9\)

D. \(4x + 6y +8 = 0\)

E. \(6x - 4y = -12\)


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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  01 Nov 2019, 05:51
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In slope-intercept form, 3x+2y-4=0 ==> y = -\(\frac{3}{2}\)x + 2

A line parallel to this line must have a slope of -1.5

5x−y+10=0 ==> y = 5x + 10 ==> To find the x-intercept, let y = 0 ==> x = -2

From the options given, C has a slope of -1.5 and x-intercept of -2, so option C is the answer.
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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  01 Nov 2019, 05:51
Line P is described by the equation 3x+2y−4=0. Which of the following lines is parallel to P and has the same x-intercept as the line 5x−y+10=0?

to be parallel the slope must be -3/2 and the y intercept should not be 2, x intercept= -2

A,B and C have the same slope

but only option C has the same X-intercept

option C is the correct option!!
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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  01 Nov 2019, 06:17
for the given line P ; \(3x + 2y - 4 = 0\).
y = -3/2x+2
slope = -1.5 and the x intercept for \(5x - y + 10 = 0\) is y =0 x=-2
out of given options
option C has slope = -1.5 i.e it is ll to line P and also has x intercept = -2
IMO C

Bunuel wrote:
Line P is described by the equation \(3x + 2y - 4 = 0\). Which of the following lines is parallel to P and has the same x-intercept as the line \(5x - y + 10 = 0\)?


A. \(6x = -4y + 8\)

B. \(-y = (\frac{3}{2})x + 5\)

C. \(3y = (- \frac{9}{2})x - 9\)

D. \(4x + 6y +8 = 0\)

E. \(6x - 4y = -12\)


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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  02 Nov 2019, 00:09
Line P is described by the equation 3x+2y−4=0. Which of the following lines is parallel to P and has the same x-intercept as the line 5x−y+10=0?

Ans: Slope of line P=-3/2
X-intercept of 5x-y+10=0 is -2

First lets check for x- intercept. Eliminate A&b
Second, lets check for slope for the remaining three eq. C is the ans

A. 6x=−4y+86x=−4y+8

B. −y=(32)x+5−y=(32)x+5

C. 3y=(−92)x−93y=(−92)x−9

D. 4x+6y+8=04x+6y+8=0

E. 6x−4y=−12
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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  26 Dec 2019, 05:00
intercept form of a line is given by x/a + y/b = 1 , a and b are x and y intercept respectively . hence, the x intercept of required line is -2 or the line passses through (-2,0). Slope of required line is -3/2
hence required line is (Y-0) = slope* (X- (-2))
----> Y = -3/2 * (X + 2)

-----> C matches
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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  25 Feb 2020, 00:04
RULE : Two lines are parallel if their slopes are equal and they have different y-intercepts

HERE , A, B and C have same slope as 3x+2y−4=0
The X intercept of 5x−y+10 =0 is 2 units. Option C satisfy this condition as per stimulus. Hence C must be the solution.
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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  11 Sep 2021, 03:06
After we have deduced that slope of the line needs to be -1.5 and x-intercept needs to be -2, is there a faster way to eliminate options/choose the right one other than just restructuring the lines to see which have slope=-1.5 and which give x=-2 after putting y=0? I went over board with time in doing that for each.
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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  11 Sep 2021, 10:03
Is going through option one by one the only way? Or there is some logical approach that would lead me to select the right answer?
Going after each option consumed a lot of time for me :(
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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink] New post  03 Jun 2023, 13:34
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Re: Line P is described by the equation 3x + 2y - 4 = 0. Which of the foll [#permalink]
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