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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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.**

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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