I just can't get my head around this, what am I doing wrong.

for example, given that,

r(t) = (1-t)r0 + t(r1)

and say we have a line segment: (-2,-1) to (1,2)

How is it that x = -2 + 3t and y = -1 +3t

r(t) = (1-t)<-2,-1> + t<1,2>

I am not seeing how this expression becomes: <-2+3t, -1+3t>

If you multiply it out, don't you get: -2 + 2t - 1 + t + t + 2t = -3 + 6t

How are you supposed to go fromSame for a line segment from (-5,3) to (0,2)

r(t) = (1-t)<-2,-1> + t<1,2>

to

<-2+3t, -1+3t>

Thanks