Answer:
The equation of the horizontal line is
.
Step-by-step explanation:
The general equation for a line having the slope and some point (x, y) is represented by the formula
, where m is the slope (<u>see below</u>), and
is a given point of the line. In this case, the point given is
.
A <em>horizontal line</em> has <em>no variation</em> in its slope (m), that is,
.

For this to be true, the term
, or
, so
. That is, the resulting line will be <em>parallel to x-axis</em> (or it could be the x-axis itself if y = 0).
A word of warning: take care that it is not the case for
, in which this would result in an <em>indeterminate form</em> for this equation, that is,
. Or, having a variation in
≠0, with
, the resulting line would be a <em>parallel line to the y-axis</em> or the y-axis itself (if x = 0), or a line of slope = ∞.
Then, the formula:
could be rewritten as
⇒
or
, and we know that the point given is
.
So, the equation of the horizontal line through
is then:
.
As can be seen in the graph attached, the line is horizontal (no variation respect to y-axis
, but it does for x-axis
≠0 ( it is different from 0 ), and the domain goes from -∞ to ∞, that is, for all values in x-axis. Notice also that the line passes through the point
.