Is #2y = 3x + 4# parallel to #-3x-2y=8#?

1 Answer
Sep 21, 2016

No they are not parallel.

Explanation:

Manipulate both so that they are in the form #y = mx + c#

Where #m# is the gradient.

'.................................................................................................
Consider #2y=3x+4#

Divide both sides by 2

#2/2xxy=3/2x+4/2" "->" "y=3/2x+2#
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Consider #-3x-2y=8#

Multiply both sides by #(-1)#

#+3x+2y=-8#

Subtract #3x# from both sides

#3x-3x+2y=-3x-8#

#2y=-3x-8#

Divide both sides by 2

#y=-3/2x-4#
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In one case the gradient is #+3/2#
In the other case the gradient is #-3/2#

As the gradients are different they are NOT parallel