Problem: The equation of the vertical line that passes through the point (4, 3).
Solution: x = 4
To understand why, please read the following step by step solution
1. Read,
understand the situation,
identify and pull out important information.
 There are infinite lines passing through the point (4,3).
 There is
only one line vertical to yaxis
passing through the point (4,3). This line is
horizontal, parallel to xaxis, and with all its points having the same "y" (3). This line crosses the
yaxis in the yintercept point.
 There is
only one line
vertical to xaxis
passing through the point (4,3), parallel to yaxis, with all its points having the same "x"
(4). It crosses the xaxis in the xintercept point.
2. Translate each of the
keywords in the problem to their appropriate
mathematical symbols.
Every point of a line is identified by its coordinates (x,y).
All points of this vertical line passing through (4,3) have the same x coordinate “4”. x = 4.
3. Set up and
solve the equation:
x = 4 The equation of the vertical line passing through (4,3). It's true only when the value of coordinate
x is “4”, for any value of "y".
4. Verify your answer.
 The slope (m) of a vertical line is undefined . Vertical lines have
no slope (it does not exist in definite concepts)!
m = RISE /RUN;
RISE = any;
RUN = 0 because when going from point (4,3) to another point on the vertical line x = 0, as we don't move horizontally (just vertically)!
slope (m) = RISE/RUN; m = RISE / 0 ; the slope is
undefined
So our line represented by
x = 4 is a vertical line!
 The equation of a vertical line is a special case of the standard form equation where
A = 0, B = 1, C = 4
0y + x = 4;
x = 4 Represents the standard form equation of the requested vertical line. No matter what the yvalue is, the xvalue is always a constant value “4”, “x” does
not change: varying "y" we move vertical to xaxis.
5. Curiosities:
 Vertical lines can’t be written in slopeintercept form (the slope is undefined and there is no yintercept).
 The xintercept point of our vertical line
is (4,0).
 Graphing
of our vertical line x = 4: Plot the given point (4,3) and the xintercept point (4,0), and draw a line through the points (4,3) and (4,0).
 In 2dimension geometry,
vertical lines have not yintercept.
 Mathematically, the only
vertical line having infinite yintercept points is
x = 0, because its points coincide with the points of yaxis. The graph of the line is the yaxis, and every
real number for y could be considered as a yintercept.
 In a 3dimensional geometry a vertical line
has only one yintercept! It does not need be perpendicular to the xaxis nor parallel to the yaxis.
 Mathematically, two parallel lines intersect at the infinity! Find the yintercept point. Think for a while (?)
4/2/2013

Carlos M.