At (0,1): 2y'=-1, y'=-½, so the tangent line has a slope -½, and the normal has a slope -1/(-½)=2.
Use slope/intercept to get the tangent line and normal line equations:
TANGENT: y-1=-x/2, y=-x/2+1
NORMAL: y-1=2x, y=2x+1
Curve is in red; the tangent line is blue and the normal line is green.