SOLUTION: Given the lines �2x + 3y = 6 and 2y + 3x = 4. What is the relationship between these lines? (Be sure to show your work and state your reason for your answer. There is no credit

Question 282935: Given the lines �2x + 3y = 6 and 2y + 3x = 4. What is the relationship between these lines? (Be sure to show your work and state your reason for your answer. There is no credit give for just a letter as the answer.)
a) Parallel
b) Intersecting at other than a 90 degree angle
c) Intersecting and perpendicular
d) No relationship

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
�2x + 3y = 6
slope =-a/b where here a=-2 and b=3
-(-2)/3=2/3
and 2y + 3x = 4
we need to rearrange
3x+2y=4
-a/b
-3/2
--3/2*2/3=-1 there fore they are perpendicular and intersecting Since perpendicular lines must cross at some point
Just for fun (not needed) let's find the intersection.
�2x + 3y = 6
3x + 2y = 4
multiply first by 3 and second by 2.
-6x+9y=18
6x+4y=8
add them
13y=26
y=2
plug 2 for y in any of the equations.
2y + 3x = 4
2*2+3x=4
3x=0
x=0
(0,2) is the intersection of the two equations.
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