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
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.
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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