Doughnut P.

asked • 10/02/14

Algebra 2, write an equation of the line. Help!

Write an equation for the line that passes through (5,6) and is parallel to x=2, what do I do? I know that when x=# it is a special line, a vertical line, and with an undefined slope. So I tried this problem out (I had other numbers in it, but I used these because I only want to make sure I can do it right.) so I used point slope form. Y-6=2-5, y-6=-3, y=3
Since the slope for x is undefined I figured there was no need to put that in there. Did I do it right?

Yohan C.

Hey Doughnut,
 
Yes, you did it right in terms of slope is undefined.  And yes, there was no need to (cannot) write y = mx + b because there will be no y-intercept from this undefined slope.
 
Even though you try to use y = mx + b, what will be the value of b when the line doesn't touch y-axis where x = 0? along the y-axis, which value of b will you use when there are infinite amount of y-values along y-axis? and value b is written like this: (x,y) ---> (0,b)
 
To make it clear from Her "Kristen A" point of view, let's go back to definition of slope.
 
slope = rise  = y  =  y2 - y1
            run     x   = x2 - x1
 
you have a point (x , y) (5, 6).  Definition of parallel line means 2 or more lines have same slope (m) and never meet each other.
 
So, let's go back to the definition of slope:  y2 - y1  =  m        
                                                              x2 - x1
 
y2 - y1 = m (x2 - x1)
 
x2 = 5 and y2 = 6
 
And you have an equation that is x = 2.  Which means x-value will not change but y-values will.
 
So, let's pick a point along x = 5. (Remember, x-value doesn't change).  Let y1 = 1
y2 - y1  =   6 - 1   = 5               
x2 - x1  =   5 - 5      0
 
As you can see, slope is undefined because denominator (x2 - x1) became 0 and you can't divide by 0.  And it is vertical since y-value changes but not x-values.
 
And yes, when question comes up like you've mentioned (The line that passes through the points (2,3) and is parallel to x=-2. would the answer be x=2? No work or anything?), no work is needed other than writing what x is (x =  ) from the given point.
 
For horizontal lines, it will be ( y =  ) where slope is 0.  (No changes in y) (changes in x)
 
I hope this won't be too difficult for you.  Good luck.
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10/03/14

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Kristen A. answered • 10/02/14

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Hi there!
 
Well, first we know that the line x=2 is just a vertical line that passes through the (2, 0) with an undefined. This problem gives us a point (5, 6) that our new line has to pass through, which we can think of at (x=5, y=6). Because our first line (x=2) is vertical and our new line (the one that passes through (5,6)) has to be parallel to it, we know that it has to be vertical (undefined slope as well). Knowing this and also knowing that the new line must pass through x=5, we can infer that the new line must be x=5. If you plot these two lines on a graph, you can see that they are parallel. 
 
I hope this makes sense. 
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Doughnut P.

Thank you. But I do not need to graph for it, simply write an equation for it, meaning y=mx+b, and the problems around this one makes you plug into point slope form and then y=mx+b. maybe you did answer my question, but I doubt thats the format it shoukd be in for this particular problem. I kind of did how it should be on my main post, but I am not sure I did it correctly.
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10/02/14

Kristen A.

You cannot put this particular equation into y=mx+b form for a couple of reasons. First, because it is vertical, the slope is undefined, which means that you cannot write "m" as an actual number. Second, because the line never crosses the y-axis (because it is vertical), a value for "b" (which is defined as the y-coordinate for the point where a line crosses the y-axis) does not exist. The only form you can write x=5 in is as it already is: x=2. Consequently, because the new line is completely vertical (as it must be because it is parallel to the line x=2), all of this must apply to it as well. Hence, the line x=5 is written just as it is: x=5. 
 
y=3 is a horizontal line which is perpendicular to the line x=2. 
 
I hope this clears things up. 
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10/02/14

Doughnut P.

Okay thanks. So lets start again. whats the work I would do for this? Would I automatically make the answer x=5 because the x1 value is 5? I know you explained but lets summarize. 
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10/02/14

Kristen A.

Hi again!
 
In the case of vertical lines, the slope is undefined so the point-slope formula doesn't really work. You simply recognize that x=5 means a line where the x-value is always 5 for any and all values of y. Like you said it is a vertical line and vertical lines are treated in a special way. 
 
In the case of horizontal lines, it's a little easier because you know the slope (m) will always be equal to 0. Hence, y=mx+b becomes y=0*x+b which then becomes y=b. In the case of a horizontal line that passes through (0,3), you would simply write y=3. 
 
 
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10/02/14

Doughnut P.

Okay, so say a new question comes up. The line that passes through the points (2,3) and is parallel to x=-2.  would the answer be x=2? No work or anything? Or should I like graph it to check whats parallel? 
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10/02/14

Kristen A.

The answer is x=2! Good job! :-) No need to graph is because all vertical lines are parallel to each other, just as all horizontal lines are parallel to each other. Make sense now? 
 
 
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10/02/14

Doughnut P.

Yes! it was actually much easier to comprehend by the simple "all vertical lines are parallel" so I just used the x point and I think I did well on my test! Thanks! 
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10/03/14

Kristen A.

That's great to hear! Congratulations!
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10/03/14

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