Question

find the parametric equations of the line that passes through the point p(2,3,4)& parallel to the xz-plane

Answer 1

To be parallel to the xz plane, y must be constant. In this case, the constant is y = 3.

There is more than one line parallel to the xz plane that passes through that point. If the z vs x slopes of the various possible slopes in the y=3 plane are denoted by m,

z - 4 = m (x - 2)