Find the equation of the tangent line at the given point on the curve.
-$x y+x=2 ;(1,1)$
A) $y=-2 x+3$
B) $y=\frac{1}{2} x+\frac{1}{2}$
C) $y=-\frac{1}{2} x+\frac{3}{2}$
D) $y=2 x-1$

Question

Quizplus · Accepted Answer

To find the tangent line, first find the derivative using implicit differentiation: $d(xy + x)/dx = d(2)/dx$. This gives $y + x(dy/dx) + 1 = 0$. Solving for $dy/dx$ at the point (1,1) gives $-2$. The tangent line is $y - 1 = -2(x - 1)$, which simplifies to $y = -2x + 3$.

Find the Equation of the Tangent Line at the Given xy+x=2;(1,1)x y+x=2 ;(1,1)xy+x=2;(1,1)

Find the Equation of the Tangent Line at the Given $x y+x=2 ;(1,1)$