@Tohar For some more detail re my previous post. Notice that I regressed Y-100 on T and T*ARM with no intercept.
So, the final equation is Y-100 = B0*T + B1*T*I(ARM=C) + B2*T*I(ARM=S), where I(ARM=C) = 1 if ARM=C, 0 otherwise. I(ARM=S) is defined similarly. So, B1 and B2 are deviations from the overall mean slope (B0). Defined this way, the slope for ARM C = B0+B1, and the slope for ARM S = B0+B2. And, to see the common intercept is 100, add 100 to both sides of the equation to get.
Y = 100 + B0*T + B1*T*I(ARM=C) + B2*T*I(ARM=S).