SOLUTION: Explain why the line x = 4 is a vertical line.

 
Let's draw a vertical line through 4 on the x axis, like this:



Now let's plot a couple of points on that line, like this:




They are the points (4,2) and (4,5). Let's label them:



Now let's get acouple more, down below the x-axis:



Those two are (4,-3) and (4,-7). Let's label them:



Now look at all those points:

(4,2), (4,5), (4,-3), (4,-7)

What do you see that they have in common?  You will
notice that the x-coordinate of every one of them is 4.

Theoretically we could get thousands more points on that 
same line. We could plot (4,9), (4,-8), (4,0), (4,-1), 
etc., etc. If we drew the graph big enough we could even 
find the points (4,100), (4,-10000), (4,746), etc.,
etc.

So the best way to say 

"The line which has all the points which have 4 as their 
x-coordinate", is to say 

"the x-coordinate always equals 4 on this line".

or "x always equals 4", 

or just plain

x = 4.

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

Another way to look at it is to think of it this way:

      x = 4

is the same as
 
 x + 0y = 4

And if we make a table of points, just
picking arbitrary values for y, say,
2, 5, -3, and -7, (I picked the same
arbitrary ones I picked above)

x | y
------
  | 2
  | 5
  |-3
  |-7

and substitute those values of y into

   x + 0y = 4       x + 0y = 4        x + 0y = 4     x + 0y = 4
 x + 0(2) = 4     x + 0(5) = 4     x + 0(-3) = 4  x + 0(-7) = 4
    x + 0 = 4        x + 0 = 4         x + 0 = 4      x + 0 = 4
        x = 4            x = 4             x = 4          x = 4  

So the points are

x | y
------
4 | 2
4 | 5
4 |-3
4 |-7 

So if we plot those four points:



and then draw a straight line through them, we have:



Do you think you understand it now why we say that vertical
line has the equation " x = 4 "?  (For that is a true statement
about every point on that line.  It's x-value or x-coordinate
is always equal to 4.

Edwin