How to find the equations of the planes from the line as intersection?

Question

The equation of the line as intersection of the two planes is: ${x=1-2t, y=3-t, z=2+8t}$

Answer 1

Eliminate $t$ and get

$$\frac{1-x}2=3-y=\frac{z-2}8.$$

Now any pair of identities defines a plane.