By inspection, the line is y = -x. However, that is not what the question is asking for.
The slope between the two given points is
.. (-2 -2)/(2 -(-2)) = -4/4 = -1
The point-slope form of the equation for the desired point is
.. y -2 = -1(x -(-2))
.. y -2 = -(x +2) . . . . . . . simplified some, still recognizable as point-slope form
