Suppose that we have a Bezier curve of degree $3$. How can I ensure that the curve will be a straight line?
So as an example take this figure
I think that we can guarantee that the red line is a straight line if the weights of $b_1$ and $b_2$ are always zero with given parameter $t \in \space [0,1]$.

The cubic Bezier curve will be a straight line when all the 4 control points are collinear.