Question #ec492

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Answer 1 · 2016-11-21T03:09:51

The slope is #22/89#

Differentiate:

#8x + 4y + 4xdy/dx + 6y^2dy/dx = 0#

Move all of the terms without #dy/dx# to the right:

#4xdy/dx + 6y^2dy/dx = -8x - 4y#

Factor out #dy/dx# on the left:

#(4x + 6y^2)dy/dx = -8x - 4y#

Divide both sides by #(4x + 6y^2)#:

#dy/dx = (-8x - 4y)/(4x + 6y^2)#

Remove a common factor of #2/2#:

#dy/dx = (-4x - 2y)/(2x + 3y^2)#

The slope, m, is the above evaluated at #(-7,-8)#

#m = (-4(-7) - 2(-8))/(2(-7) + 3(-8)^2)#

#m = (44)/(178) = 22/89#