SOLUTION: Name three points on the line represented by x=4. Then explain why, when we connect these points, the line goes straight up and down and does not slant to the left or right.

Algebra ->  Linear-equations -> SOLUTION: Name three points on the line represented by x=4. Then explain why, when we connect these points, the line goes straight up and down and does not slant to the left or right.      Log On


   

Question 356324: Name three points on the line represented by x=4. Then explain why, when we connect these points, the line goes straight up and down and does not slant to the left or right.
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

x = 4

(4, 2) (4,4) (4.-4) points of the line

The line drawn, to connect points on the line, goes straight up and down 

(or is perpendicular to the x = axis because the x value must always remain the same, 

according to the statement, as in this case, x = 4

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the line (in green) whose equation is x = 4:



Here are three points on that line:




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.


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

Why does the line goes straight up and down and does not slant to the left or right?
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:


 
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