Question 356324
<pre>
Here's the line (in green) whose equation is x = 4:

{{{drawing(400,400,-10,10,-10,10,

graph(400,400,-10,10,-10,10), green(line(4,11,4,-11)) )}}}

Here are three points on that line:

{{{drawing(400,400,-10,10,-10,10,
graph(400,400,-10,10,-10,10), green(line(4,11,4,-11)),
line(4+.1,3,4-.1,3), line(4+.1,3+.1,4-.1,3-.1), line(4+.1,3-.1,4-.1,3+.1),   locate(4,3,"(4,3)"),

line(4+.1,-6,4-.1,-6), line(4+.1,-6+.1,4-.1,-6-.1), line(4+.1,-6-.1,4-.1,-6+.1),   locate(4,-6,"(4,-6)"),


line(4+.1,8,4-.1,8), line(4+.1,8+.1,4-.1,8-.1), line(4+.1,8-.1,4-.1,8+.1), locate(4,8,"(4,8)")


)}}}


Look at all those ordered pairs, labels for points, (4,8), (4,-6), and (4,3).
See all those 4's?  All three have a 4 for their x coordinate.  Did you know
that's why the equation x = 4 is the equation of that vertical green line?  The
equation "x equals 4" just tells us what is true about every ordered pair
representing a point on that line.  

                   x = 4
just says:

               x is always equal to 4

which means:

        The x-coordinate of every point on that green line = 4

That's why x = 4 is its equation.  It tells us what is true about the 
x-coordinate of every point on that line.  We can't say that about
any other line except that green one.


---------------------------------------------------------

</pre>
Why does the line goes straight up and down and does not slant to the left or right?
<pre>
Because if it slanted to the left or right, its x-coordinates would not be all
equal to 4 like they are on the green line above.  If we drew a slanted green
line like this:

{{{drawing(400,400,-10,10,-10,10,
graph(400,400,-10,10,-10,10), green(line(-3,-12,7,13)),
line(3+.1,3,3-.1,3), line(3+.1,3+.1,3-.1,3-.1), line(3+.1,3-.1,3-.1,3+.1),   locate(3,3,"(3,3)"),

line(-1+.1,-7,-1-.1,-7), line(-1+.1,-7+.1,-1-.1,-7-.1), line(-1+.1,-7-.1,-1-.1,-7+.1),   locate(-4,-7,"(-1,-7)"),


line(5+.1,8,5-.1,8), line(5+.1,8+.1,5-.1,8-.1), line(5+.1,8-.1,5-.1,8+.1), locate(5,8,"(5,8)")


)}}}
 
We couldn't say all the ordered pairs which represent points on that graph
have their x-axis equal to 4. Because as you see, those points have all
different x-coordinates.  And they are determined by a different equation.

All the points which have their x-coordinates equal to 4 are all on that
vertical line and none of them are anywhere else.  That's why "x = 4" is
all you need to tell the story about every point on that line having its
x-coordinate equal to 4.

Edwin</pre>