Question 119182
Please don't write your questions in all CAPs.


A line perpendicular to the x-axis is a line whose points all have the same x-coordinate.  Therefore, if the line passes through (3,4), the x-coordinate of all the points on the line must be 3.  The set of points that comprise the line therefore is the set of all ordered pairs (3, y) for all real numbers y.  The equation {{{x=3}}} defines the line.


The standard form of a line is {{{Ax+By=C}}}, so putting {{{x=3}}} into standard form would result in {{{x+0y=3}}}.  Note that the slope of such a line would be undefined because the slope of a line in standard form is defined as {{{-(A/B)}}} and our equation would have a zero in the denominator.  This result is consistent with our understanding of the slope of a vertical line.


Hope this helps.