equation of line

Question

Find the equation of line with a slope of 458 which passes through the point 4-5-8 or 3+4+8

Answer 1

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.