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

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

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• You cannot express a line in 3d space as a cartesian equation. Aug 28, 2021 at 1:54

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 $$x=1$$.