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Which of the following describes the graphs of 2x – 3y = 9 and 6x – 9y = 18:...

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pizza35 | Student, Undergraduate | eNoter

Posted August 21, 2012 at 6:13 PM via web

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Which of the following describes the graphs of 2x – 3y = 9 and 6x – 9y = 18:

parallel
coinciding
perpendicular
none of these

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 21, 2012 at 6:37 PM (Answer #1)

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The two lines given are 2x - 3y = 18 and 6x - 9y = 18

2x - 3y = 18

=> y = (2/3)x - 6

6x - 9y = 18

=> y = (6/9)x - 2 = (2/3)x - 2

The slope of the lines is the same, therefore they are parallel lines.

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dalla00000 | Student, Undergraduate | eNotes Newbie

Posted August 21, 2012 at 9:29 PM (Answer #2)

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the lines 2x - 3y =18 .......#1     and 6x - 9y =18...........#2

using the equation y = mx + c

where m is the gradient

from #1                            from #2

2x - 3y =18                      6x - 9y =18

2x - 18 =3y                       6x -18=9y

dividing through by 3          dividing through by 9

2x/3 - 6 =y    =>m=2/3                   2x/3 - 2 =y   =>m=2/3

therefore since m=2/3 is the same for both equations hence the lines are parallel

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