The x-intercept of k is 0.

Question

The x-intercept of a line K is ZERO means?

Does this also mans this line

Does the line shown in orange which is parallel to X axis also qualifies a line whose X intercept is 0? Because this line is also not intercepting the X axis anywhere?

Answer 1

A line with an $x$-intercept of zero means that it crosses the $x$ axis at the point $(0, 0)$. Recall that $x$-intercepts are those points of the form $(x, 0)$.

Now, consider the line $y = k$ for nonzero $k$. This line is parallel to the $x$ axis (and thus has slope zero) but only contains points of the form $(x, k)$ where $k$ is fixed. Drawing a picture shows that it does not cross the $x$-axis and so there are no $x$-intercepts. Not infinitely many $x$-intercepts. No $x$-intercepts.

TLDR: If it doesn't cross the $x$-axis then there are no $x$-intercepts.

Answer 2

$x$ intercept of a line is generally the distance from the origin at which the line cuts $x$ axis. In your case the orange line never cuts/intersect $x$ axis so there is no $x$ intercept