what type of lines are these?

Eugenio said:
If 2 parallel lines have an intersection, then they are the same line. A line can be written with infinite values of A, B, and C. For example:
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Two lines cannot be the same for otherwise they would not be two.
 
pka said:
Two lines cannot be the same for otherwise they would not be two.
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Thank youuu.
Thank youuuuuu.
That is help, that is really helpful!.
Every tutor in the forum knows i do the work and expect no easy answers!. I havexspent two days working non-stop on this problem.Just a guide and when I get stuck and just clear direction is what i need.
Thank you so much to you pka and Eugenio.
 
Eugenio said:
If 2 parallel lines have an intersection, then they are the same line. A line can be written with infinite values of A, B, and C. For example:

2x + 3y = 5 and 4x + 6y = 10 and -6x - 9y = -15

are the same line. If you multiply every term of the equation by the same factor different from zero, you will get the same line.

You don´t need to work with the slope if you want to determine if 2 lines are parallel or perpendicular. If you have

[MATH]A_1x+B_1y=C_1[/MATH]
and

[MATH]A_2x+B_2y=C_2[/MATH]
Then, if [MATH]A_1*B_2=A_2*B_1[/MATH] they are parallel. If [MATH]A_1*A_2+B_1*B_2=0[/MATH] they are perpendicular. If they are parallel, and they share one point, they are the same line.
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Thanks a lot. Real good
 
Eugenio said:
If 2 parallel lines have an intersection, then they are the same line. A line can be written with infinite values of A, B, and C. For example:

2x + 3y = 5 and 4x + 6y = 10 and -6x - 9y = -15

are the same line. If you multiply every term of the equation by the same factor different from zero, you will get the same line.

You don´t need to work with the slope if you want to determine if 2 lines are parallel or perpendicular. If you have

[MATH]A_1x+B_1y=C_1[/MATH]
and

[MATH]A_2x+B_2y=C_2[/MATH]
Then, if [MATH]A_1*B_2=A_2*B_1[/MATH] they are parallel. If [MATH]A_1*A_2+B_1*B_2=0[/MATH] they are perpendicular. If they are parallel, and they share one point, they are the same line.
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Can two lines be concurrent or do we need more than 2?
 
eddy2017 said:
Can two lines be concurrent or do we need more than 2?
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Two days working on an exercise with an easy solution .
For Gods sake. Stop showing off what you know. We know you know. Members like me want clear help. Stay off my threads plase. You re making me work and work and confusing me and then not following on posts. Don't answer me any more. There are others in this forum who might not a little less but are great teachers!. And thst is what I need. I don't need savants and pn top of tvst they give actitudes. You know where is a good lake?. Go take a flying jump on it.
Stay off
 
eddy2017 said:
the question has not been answered!!!! …
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Hi Eddy. If you mean the exercise has not been answered (versus a question about it that you've asked), then you should know that I wasn't trying to give you the answer to the exercise. You told me that you wanted "direction" and "hints", not the answer.

I'd posted why the equations that you'd graphed (expecting to see perpendicular lines) were not perpendicular. One of your equations had the wrong slope.

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eddy2017 said:
i have been doing the work watching tutorial and posting it, where is your help? …
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Did you read my quotation of post #1?

You often start threads telling us how you'd like to begin an exercise. Then you ask for confirmation of your thoughts.

If you have an idea about how to begin an exercise, then why not try it? You don't need to ask us if your ideas are okay, first. Just go for it. If you get stuck, then show us what you've tried.

?
 
eddy2017 said:
… Stay off my threads plase …
… don't need savants and pn top of tvst …
… Stay off
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Eddy, that's not clear at all. Which specific members are you asking to stay off your threads?

:confused:
 
When mathematicians say something like, "They are both the same line", they mean both equations plot as the same line.

Sloppiness in academic language/notation is something we all need to get used to.

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Otis said:
Did you read my quotation of post #1?

You often start threads telling us how you'd like to begin an exercise. Then you ask for confirmation of your thoughts.

If you have an idea about how to begin an exercise, then why not try it? You don't need to ask us if your ideas are okay, first. Just go for it. If you get stuck, then show us what you've tried.
Click to expand...
 
i am sorry i get so mad when i'm not following or can't seem to get something straight. i know you are folowing different threads, and sometimes i seems like some of you are following and then repeat or ask something we have been over before ...but that is ok. i need to be patient. . i work and study and have a family so it is difficult. no one needs to stay off my threads. i take it back. that was in the heat of the moment. i apologize. you all have helped me a lot!
but if you see i am not seeing the pic it is because i do not see it. sometimes i may even ask if this or that tutorial is fitting for this or that type of question.
okay, thanks, have a good evening!
 
eddy2017 said:
This is the sufficient condition for two planer lines to be perpendicular to each other.

But why?. I need to understand the reason why they are!. [perpendicular to each
other and and intercepting]
Drop me a hint at least.

And pka is not agreeing with the way I performed it
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Visit:

Proof: perpendicular lines have negative reciprocal slope | Analytic geometry (video) | Khan Academy

Sal proves that perpendicular lines have opposite reciprocal slopes using triangle similarity.
www.khanacademy.org
 
The phrase 'concurrent lines' is another example in mathematics where there is more than one definition. Some people say you need three or more lines intersecting at a point, to attain concurrency; others say two or more. (Those who don't say probably don't care.)

I've rarely seen the adjective 'concurrent' used, in the context of discussing lines. I see the phrase 'interecting lines', mostly, so I tend to think that concurrent lines are any lines intersecting at a single point.

Maybe 'concurrent lines' is more-commonly used in classical geometry (which I flunked).

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Otis said:
The phrase 'concurrent lines' is another example in mathematics where there is more than one definition. Some people say you need three or more lines intersecting at a point, to attain concurrency; others say two or more. (Those who don't say probably don't care.)

I've rarely seen the adjective 'concurrent' used, in the context of discussing lines. I see the phrase 'interecting lines', mostly, so I tend to think that concurrent lines are any lines intersecting at a single point.

Maybe 'concurrent lines' is commonly used in classical geometry (which I flunked).

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Thanks, Otis . Yes, that is what I have read online. Three lines.

This is from an article I found online:

"The one-dimensional line made up of infinite points that follow one another in the same direction is called a straight line. Concurrent, on the other hand, is an adjective that refers to that which concurs (that is, that meets with others of its kind in the same place)
These definitions allow us to approach the notion of a concurrent line. Concurrent lines are three or more lines that are in the same plane and that have a common point. This means that the concurrent lines pass through the same point, unlike parallel lines that do not have points in common, they are equidistant from each other and do not have the possibility of crossing even when they are prolonged indefinitely. Both properties, therefore, are exclusive: if the lines are parallel, they are not concurrent, and vice versa".
 
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Otis said:
When mathematicians say something like, "They are both the same line", they mean both equations plot as the same line.

Sloppiness in academic language/notation is something we all need to get used to.

  \;
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Your comment was very helpful in helping me understand the graphs when I plotted it on Desmos. Thanks for the clarification.
 
eddy2017 said:
“... Both properties, therefore, are exclusive: if the lines are parallel, they are not concurrent, and vice versa".
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Seems to me the statement above works with two lines as well as with three, so I don’t know why some people say it doesn’t apply to a system of two linear equations. Their perspective on ‘concur’ puzzles me, also. Two people can concur on something. Why does it have to be with “others” (plural).

Seems, too, that I don’t care enough to research the reasons, heh.

If you scroll past the first example system on the page below, you’ll see systems labeled as Consistent vs Inconsistent and equations in a consistent system labeled as Independent vs Dependent. That’s the terminology I’m accustomed to seeing, when comparing systems of linear equations.

Systems of Linear Equations: Two Variables | College Algebra

courses.lumenlearning.com courses.lumenlearning.com

?
 
eddy2017 said:
Thanks, Otis . Yes, that is what I have read online. Three lines.

This is from an article I found online:

"The one-dimensional line made up of infinite points that follow one another in the same direction is called a straight line. Concurrent, on the other hand, is an adjective that refers to that which concurs (that is, that meets with others of its kind in the same place)
These definitions allow us to approach the notion of a concurrent line. Concurrent lines are three or more lines that are in the same plane and that have a common point. This means that the concurrent lines pass through the same point, unlike parallel lines that do not have points in common, they are equidistant from each other and do not have the possibility of crossing even when they are prolonged indefinitely. Both properties, therefore, are exclusive: if the lines are parallel, they are not concurrent, and vice versa".
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"Concurrent" just means intersecting in one point, and applies to any number of lines: https://mathworld.wolfram.com/Concurrent.html

It's most interesting when three or more lines are concurrent, as it is usual for any two lines to be concurrent (parallel lines being special): https://www.mathopenref.com/concurrent-lines.html

Wikipedia gives many such interesting examples: https://en.wikipedia.org/wiki/Concurrent_lines

Your source is not very well-written.
 
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