Does the equation #3x+5y=0# represent a direct variation and if so, identify the constant of variation?

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Answer 1 · 2016-05-13T18:52:54

The constant of variation is #3/5#
I will let you decide if this is positive or negative. See explanation as to why.

Given: # 3x+5y=0#

Subtract #3x# from both sides

#3x-3x+5y=0-3x#

#0+5y=-3x

#5y=-3x#

Divide both sides by 5

#5/5xxy=-3/5x#

But #5/5=1#

#y=-3/5x#

If you wish the #x# to be positive: multiply both sides by #(-1)#

#-y=+3/5x#

The constant of variation is #3/5#