Cartesian equation of a line parallel to the X-axis in 3D

Question

Suppose the vector equation of a line parallel to the X-axis is

x = 1 + t
y = 2
z = 3

How do I rewrite this into a cartesian equation like the below example?

ƛ = x + 1 = 1 - y = z - 1

Answer 1

A line in 3-D space cannot be expressed as a cartesian equation the way it could be expressed in 2-D space.

Take for example 1-D space. Suppose we have $x=1$. We just have one point, $(1)$. Next, go into 2-D space, and $x=1$ is a vertical line, and no longer a point (since any $y$-value will satisfy $x=1$. Then, move into 3-D space, where $x=1$ is a plane, since any $z,y$-values will satisfy $x=1$.