Equation of line :
(y - 4)/(0 - 4) = (x - 0)/(- 8 - 0)
(y - 4)/(-4) = x/(-8)
y - 4 = x/2
y = x/2 + 4.
For reflection in the y - axis, replace x by - x, that is
y = (-x)/2 + 4 = - x/2 + 4
For reduction along the x - axis, multiply x by (1/k). Now k = 1/2, so multiply x by 2.
So y = (- 2x)/2 + 4 = - x + 4.