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The equation of the vertical line that passes through the point (4, -3)

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3 Answers

A vertical line passing through the point (4, -3) means that for any value of y, x is always going to be equal to 4; the formula may be generally written as x = a where a is the x-intercept.. An x-intercept is the value of x when y = 0. As we already stated, for any value of y, x = 4. Therefore, this vertical line will pass through the point (4,0). You can write the equation as x = 4. Graphing this equation in a graphing calculator requires you to "trick" the graphing calculator because in the "graph" menu you only have the option of writing in equations in the form y =, which you can't do for this problem. If out try to type in y1=x-4, you won't get a vertical line, you will get a line with as slope of 1 that passes through the point (0,-4). What you need to do is type the equation in as follows y1= (really big number)(x-4) = 100000(x-4), thereby giving you a "workable" vertical line.

Vertical lines: lines that run up and down.  If you are standing up then you are vertical.  On a graph the x-axis has little marks that run up and down or "vertical."  Since the x-axis has lines that run vertical then if you have a point use you x-ordinate (x number).   Therefore; in the point (4, -3), your vertical line is x = 4.

In the point (2, 10), can you determine the vertical line ...

 

 

 

 

Right you figured it out x = 2.

 

For vertical line just take the other number and write y =.

Good luck.

Problem: The equation of the vertical line that passes through the point (4, -3).

Solution:  x = 4    

To understand why, please read the following step by step solution

1. Read, understand the situation, identify and pull out important information.

  • There are infinite lines passing through the point (4,-3).
  • There is only one line vertical  to y-axis passing through the point (4,-3). This line is horizontal, parallel to x-axis, and with all its points having the same "y" (-3). This line crosses the y-axis in the y-intercept point
  • There is only one line vertical  to x-axis passing through the point (4,-3), parallel  to y-axis, with all its points having the same "x" (4)It crosses the x-axis in the x-intercept point. 

2. Translate each of the keywords in the problem to their appropriate mathematical symbols.

Every point of a line is identified by its coordinates (x,y). All points of this vertical line passing through (4,-3) have the same x coordinate “4”.   x = 4.

3. Set up and solve the equation:

x = 4     The equation of the vertical line passing through (4,-3). It's true only when the value of  coordinate x is “4”, for any value of "y".

4. Verify your answer.

  • The slope (m) of a vertical line is undefined . Vertical lines have no slope (it does not exist in definite concepts)!

m = RISE /RUN;
RISE = any;
RUN = 0     because when going from point (4,-3) to another point on the vertical line  x = 0,  as we don't move horizontally (just vertically)!   

slope (m) = RISE/RUN;   m = RISE / 0 ;  the slope is undefined    

So our line represented by x = 4  is a vertical line!

  • The equation of a vertical line is a special case of the standard form equation where

               A = 0, B = 1, C = 4

0y + x = 4;

x = 4   Represents the standard form equation of the requested vertical line. No matter what the y-value is, the x-value is always a constant value “4”, “x” does not change:  varying "y" we move vertical to x-axis.

5. Curiosities:

  • Vertical lines can’t be written in slope-intercept form (the slope is undefined and there is no y-intercept).
  • The x-intercept point of our vertical line is (4,0).
  • Graphing of our vertical line x = 4: Plot the given point (4,-3) and the x-intercept point (4,0), and draw a line through the points (4,-3) and (4,0). 
  • In 2-dimension geometry, vertical lines have not y-intercept.
  • Mathematically, the only vertical line having infinite y-intercept points is x = 0, because its points coincide with the points of y-axis. The graph of the line is the y-axis, and every real number for y could be considered as a y-intercept.
  • In a 3-dimensional geometry a vertical line has only one y-intercept! It does not need be perpendicular to the x-axis nor parallel to the y-axis.
  • Mathematically, two parallel lines intersect at the infinity! Find the y-intercept point. Think for a while (?)

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