Find eqn of Tangent Line to graph- Implicit Differentiation

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Homework Statement


Find the equation of the tangent line to the graph of the given equation at the indicated point.

##xy^2+sin(πy)-2x^2=10## at point ##(2,-3)##

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The Attempt at a Solution



Please see attached image so you can see my thought process. I think it would make more sense that typing it out.
My solution is ##\frac{7}{-12-π}## But I don't think this is correct. The ##πy## inside the argument of the sin function is throwing me off.
 

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opus
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Image.

Let me add that I know this problem isn't finished. Up to my current position is where I'm seeking clarification.
Thanks!
 

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I cannot read your image without further processing. The denominator looks o.k. but the nominator seems to be wrong. Your slope is roughly ##-\frac{1}{2}## whereas the plot looks more like ##\pm 0##.
 
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That's embarrassing :DD
So we have ##\frac{-1}{-12-π}## and this makes more sense now. So this is the slope of the tangent line at (2,-3) and now I can continue on hopefully without forgetting how to add.
 
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