Let vector A=<4,5,8> and vector B=<3,4,8>.
These vectors have the same z coordinate so the line lies in the x-y plane.
That means we can work out the equation of the line just using the x and y coordinates.
Slope in x-y plane=(5-4)/(4-3)=1. y-4=x-3, y=x+1.
We can write the 3D equation of the line as y=x+1, z=8.