Find the slope of the tangent line to the graph of -2y + 8x^2 = -7x + 9y^2 - 29 at (2,-3)

Answer:Step-by-step explanation:Take the derivative of all terms with respect to x:-2(dy/dx) + 16x = -7 + 18y(dy/dx).  Grouping the (dy/dx) terms on the left, we get:(dy/dx)(-2 - 18y) = -7 - 16x, or                  -7 - 16xdy/dx = ------------------                 -2(1 + 18y)Substituting 2 for x and -3 for y, we obtain the desired derivative:                  -7 - 16x          -7 - 32           -39dy/dx = ------------------ = --------------- = ----------- = -0.368                 -2(1 + 18y)       -2(1 - 54)        106