Question 991364
Differentiate implicitly,
{{{(dx-dy)/(x-y)=xdy+ydx}}}
{{{dx-dy=(x-y)xdy+(x-y)ydx}}}
{{{-(x-y)xdy-dy=(x-y)ydx-dx}}}
{{{(-(x-y)x-1)dy=((x-y)y-1)dx}}}
{{{dy/dx=((x-y)y-1)/(-(x-y)x-1)}}}
So then,
{{{dy/dx=((1-0)0-1)/(-(1-0)1-1)}}}
{{{dy/dx=(-1)/(-1-1)}}}
{{{dy/dx=-1/(-2)}}}
{{{dy/dx=1/2}}}
Use the point-slope form of the tangent line,
{{{y-0=(1/2)(x-1)}}}
{{{y=(1/2)x-1/2}}}
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