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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