To obtain the slope of this TL at (2,2), differentiate xy=4 with respect to x:
x(dy/dx) + y(dx/dx) = 0. Then x(dy/dx) = -y, and (dy/dx) = -y/x.
At (2,2), this slope is -2/2, or -1.
Then the eqn of the TL to the curve xy=4 is y-2 = -1(x-2) = -x+2
Thus, y = 2 - x + 2, or y = -x + 4 (answer)
