Question 1080222
To find the slope, calculate the derivative at the point.
Using implicit differentiation,
{{{2xdx+2ydy=0}}}
{{{ydy=-xdx}}}
{{{dy/dx=-x/y}}}
So at (2,-4),
{{{m=dy/dx=-2/-4=1/2}}}
Using the point-slope form of a line,
{{{y-(-4)=(1/2)(x-2)}}}
{{{y+4=x/2-1}}}
{{{y=x/2-5}}}
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*[illustration dr1.JPG].