SOLUTION: We are presently graphing linear equations. I am totally lost. gWe have to anwer a response to: Why the line x=4 is a vertical line? How do begin? How do I solve this?

Question 214797: We are presently graphing linear equations. I am totally lost. gWe have to anwer a response to:
Why the line x=4 is a vertical line? How do begin? How do I solve this?
Found 3 solutions by stanbon, jsmallt9, drj:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Why the line x=4 is a vertical line? How do begin? How do I solve this?
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Any line can be graphed if you can find two points on the line.
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Two points on your line would be (4,0) and (4,5)
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Plot those two points on a coordinate system.
Draw a line thru them.
Notice that the line passes thru all the points where x = 4.
Notice that the line is perpendicular to the x-axis.
Notice that the line is vertical.
Cheers,
Stan H.
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
First we need to understand that the graph of an equation represents all the points whose coordinates fit the equation. In other words the ordered pair coordinates of every point on your graph must make the equation true.

So we have to ask ourselves: "What ordered pairs will fit x=4?" Well it should be obvious that the x-coordinate must be a 4 in order to fit this equation. But what about the y-coordinate? There is no "y" in the equation!? What y-coordinates fit an equation which has no "y"? Answer: They ALL do!! Since there is to "y" in the equation we do not need substitute the y-coordinate into the equation to see if the ordered pair fits the equation. So as long as the x-coordinate is 4, the y-coordinate can be ANY number and the order pair still fits the equation x=4! So the solutions to x=4 are all the points with an x-coordinate of 4.

And where on the coordinate plane do we find all these points with an x-coordinate of 4? With some logic or after plotting several of these points, it should become clear that these points form a vertical line 4 units to the right of the y-axis.

Other clues to the graph of this type of equation are:
The slope-intercept form of the equation of a line is: y = mx + b
Equations of the form x = [some-number] (like x=4), have no "y" and without a "y" it is impossible to transform the equation into slope-intercept form.
Slope is rise/run
Vertical lines have a run of 0 since they do not go sideways at all.
With a run of 0, slope is not even defined for vertical lines (since dividing by zero is undefined)

Fact #2 (equations of the form x = [some-number] have no slope-intercept form) and #5 (vertical lines have no defined slope) are connected. If one is true then other is also true.
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
We are presently graphing linear equations. I am totally lost. We have to anwer a response to: Why the line x=4 is a vertical line? How do begin? How do I solve this?

Step 1. A line is given in slope-intercept form as y=mx+b where m is the slope and b is the y-intercept at point (0,b). The y-intercept intersects the y-axis when x=0. When we substitute x=0 into y=mx+b we get y=b. So the point (0,b) is a point in the line. Another point in the line is when y=0 then 0=mx+b or x=-b/m.

Step 2. Now, why is the line vertical for x=4. Note y can be any value as long as it has it's x-coordinate to be 4.
For example, consider the the points (4, 0), (4, 1), and (4, -1) plot it in the graph and draw a line through these points. What all these points have in common is that they have the x-coordinate to be 4. In fact, you can have many y-values with an x-coordinates of 4 or x=4.

Now if y=4, then you have many points with y-coordinate of 4. That is, points (0,4), (-1,4) and (1,4) will have the same y=4 and different values of x. When you plot these points then these points, the line will be horizontal.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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