Question

find the equation of the tangent line at the give point on the curve. xy + x = 2 (1,1)

Answer 1

take the derivative get
\[y+xy'+1=0\] replace \(x\) and \(y\) by 1, solve for \(y'\) to get the slope
then use the point slope formula

Answer 2

alright thank you.

Answer 3

so the derivative would be : y'=(-y-1)/x

y'(1,1)=-1-1/1
y'(1,1)=-2

so slope would be :

y-y1=mtan(x-x1)
y-1=-2(x-1)
y=-2x+3

Is this correct?