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

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 Click here to see ALL problems on Linear-equations Question 156607: Explain why the line x = 4 is a vertical line. Found 3 solutions by Alan3354, Edwin McCravy, gonzo:Answer by Alan3354(47455)   (Show Source): You can put this solution on YOUR website! Explain why the line x = 4 is a vertical line. -------------------- The x and y axes are perpendicular. Usually, the x-axis is shown as horizontal and the y-axis as vertical. So vertical means parallel to the y-axis. =================================== For the function x = 4, there is no mention of y. This means that regardless of the value of y, x=4. This is a line thru the point (4,0), and thru the point (4,y), no matter what y is. This is a line parallel to the y-axis and 4 units to the right of it (as it's usually drawn). Parallel to the y-axis is vertical. Answer by Edwin McCravy(13211)   (Show Source): You can put this solution on YOUR website! Edwin's explanation: 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``` Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website! if you plot for any value of y, then x = 4 always. the line formed is parallel to the y axis because that line and the y axis will never meet because they will always be 4 units apart. the y axis is perpendicular to the x axis by definition. the line x = 4 is therefore perpendicular to the x axis because if a line is perpendicular to another line than it's parallel line is also perpendicular to that line. this is based on a geometric postulate or proof that states that the corresponding angles are equal. if one parallel line intersects another line at 90 degrees then the other parallel line intersects that same line at 90 degrees as well.