I think I got it

Would you simply add the parametric equation of the helix to the parametric equation of the line?

l(t)=<1+t,1+2t,1+3t> and h(t)=<cost,sint,t>

so x(t)=1+t+cost, y(t)=1+2t+sint, z(t)=1+3t+t=1+4t

I believe this works. Someone correct me if I'm wrong.