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
, where m is the slope (<u>see below</u>), and  is a given point of the line. In this case, the point given is
 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,  .
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For this to be true, the term  , or
, or  , so
, 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).
. 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,
, in which this would result in an <em>indeterminate form</em> for this equation, that is,  . Or, having a variation in
. Or, having a variation in  ≠0, with
≠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 = ∞.
, 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
 could be rewritten as  ⇒
 ⇒  or
 or  , and we know that the point given is
, and we know that the point given is  .
.
So, the equation of the horizontal line through  is then:
 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
, 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
 ≠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  .
.