I was wondering if anyone would be able to show me how to do the very end of this sum

p(t) = p1 + t(p2 - p1)

Find the equation of each of the following lines

(a) The line passing through [0,1,2] and [0,2,4].

this is my working out

p(t) = [0,1,2] + t([0,2,4] - [0,1,2]

p(t) = [0,1,2] + t([0,1,2])

p(t) = [0,1,2 + t + t2].

but the answer is [0,1+ t, 2 +2t] could someone please explain to me why its written in this order?