Find the equation of the tangent line at the given point on the curve.
-2xy - 2x + y = -14; (2, -2)
A) $y=\frac{6}{5} x-\frac{22}{5}$
B) $y=-\frac{5}{6} x+\frac{22}{6}$
C) $y=-\frac{6}{5} x+\frac{22}{5}$
D) $y=\frac{5}{6} x-\frac{22}{6}$

Question

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the slope of the curve at the given point. The slope of the curve is given by the derivative of the function.$f(x,y) = 2xy - 2x + y$$\frac{dy}{dx} = \frac{2y - 2}{2x + 1}$At the point (2, -2), the slope of the curve is:$\frac{dy}{dx} = \frac{2(-2) - 2}{2(2) + 1} = -\frac{6}{5}$So, the equation of the tangent line is:$y - (-2) = -\frac{6}{5}(x - 2)$$y + 2 = -\frac{6}{5}x + \frac{12}{5}$$y = -\frac{6}{5}x + \frac{22}{5}$

Find the Equation of the Tangent Line at the Given y=65x−225y=\frac{6}{5} x-\frac{22}{5}y=56​x−522​

Find the Equation of the Tangent Line at the Given $y=\frac{6}{5} x-\frac{22}{5}$