Find the equation of the line that contains the point (6,-2) and is perpendicular to the line y=-2x+8?

The given line has slope -2, so the desired line will have a slope that is the negative reciprocal of that:
  m = -1/(-2) = 1/2

The point-slope form of the equation of the line can be written as
  y = m(x -h) +k
for a line with slope m through point (h, k). For your m=1/2, (h, k) = (6, -2), the equation of your line is
  y = (1/2)(x -6) -2
  y = (1/2)x -5

The equation of the desired line is ...
  y = (1/2)x -5