What is the equation of a line passing through (5,4) and (5,-6)?

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The discussion revolves around finding the equations of lines based on given points and slopes. A line with a slope of zero is horizontal, resulting in the equation y=4 for the point (5,4). Conversely, a line with an undefined slope is vertical, leading to the equation x=-2 for the point (-2,4). The participants express confusion about determining slopes and equations for additional points, particularly when slopes are calculated as zero or undefined. Ultimately, the conversation highlights the simplicity of these concepts once clarified.
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Write an equation of a line with a slope of 0 and passing through the point (5,4).

Write an equation of a line with an undefined slope and passing through the point (-2,4).


I know how to do this type of thing but these two questions have stumped me.

If the slope of the first one is zero, it'll be a horizontal line. That means the equation will look something like this: y= some number right?

If so, what do I do with the (5, 4)? Do I just graph that point and see where it is as far as y goes? If that's what I'm to do...*Looks at a graph* y= 4? Now that I think about it, I didn't need the graph so that either means it's really easy or really wrong.:smile:

As for the second one, if the slope is undefined it would be vertical and would look like this: x= some number. Would it be the same way, again, assuming I did the first one right? x= -2?

EDIT: Write an equation of a line that passes through (9,-5) and (3,-5).

The slope is 0/-6, right? Does that make it undefined or 0? I can't tell the difference. What if the answer was -6/0? Which would that be?

As for writing the equation, it would be x or y, whichever it is according to whether it's undefined or zero...y/x = Aw, geez, I don't even know how to go about this one...

Write an equation of a line that passes through the points (2,3) and (2,-6).

slope = -9/0

I have two points...so, what I would do is...hm, would graphing them help me or not?
 
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Your answers are correct. So maths can be simple...
 
Thanks.:smile:

I suppose I was a bit late with my edit...:smile:

Write an equation of a line that passes through (9,-5) and (3,-5).

The slope is 0/-6, right? Does that make it undefined or 0? I can't tell the difference. What if the answer was -6/0? Which would that be?

As for writing the equation, it would be x or y, whichever it is according to whether it's undefined or zero...y/x = Aw, geez, I don't even know how to go about this one...*Pulls out her notes* I can't find anything referring to this type of problem...Method 1: If you are given the equation of the line, put the equation in slope intercept form. Nope, that's not it. Method 2: If you are given the graph of the equation, count the change in y and the change in x on the graph paper to determine the slope. Nope, not right either. Method 3: Nope, that only shows how to find the slope (I used method three for this one...) but it doesn't show what to do next...

Write an equation of a line that passes through the points (2,3) and (2,-6).

slope = -9/0

I have two points...so, what I would do is...hm, would graphing them help me or not?
 
Look at the points. What do you see?
 
I don't know...I don't know what I'm supposed to be seeing. I've looked at them already so if I wasn't seeing it before I'm not seeing it now.:shy: :smile:
 
Never mind, got it. ^_^
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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