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Can two lines having the same slopes intersect?

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Can two lines having the same slopes intersect?

by gmat_perfect » Sat Mar 27, 2010 4:03 am
I have a doubt whether two lines that have same slopes can intersect.

What is my understanding:

1. Say the two lines have the same slope of 2.
2. If one line is over another line, then those two lines intersect in every point.

I think that in that case those lines intersect.

Am I right ?

Math gurus, please help.

Thanks in advance.
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by eaakbari » Sat Mar 27, 2010 4:08 am
If two lines have the same slope they are either parallel or we are talking about the same line, which I assume is what you meant by "intersecting at all points".
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by sanju09 » Sat Mar 27, 2010 5:32 am
gmat_perfect wrote:I have a doubt whether two lines that have same slopes can intersect.

What is my understanding:

1. Say the two lines have the same slope of 2.
2. If one line is over another line, then those two lines intersect in every point.

I think that in that case those lines intersect.

Am I right ?

Math gurus, please help.

Thanks in advance.
Recall basics here...

If a system of linear equation in two variables like a x + b y + c = 0 and a' x + b' y + c' = 0 represents two straight lines, then observe the coefficient's behavior and conclude

If a/a' ≠ b/b', then the two straight lines would intersect in exactly one point. Algebra calls it a unique solution case.

If a/a' = b/b' ≠ c/c', then the two straight lines are distinct and parallel, and hence would never intersect. Algebra calls it a no solution case.

If a/a' = b/b' = c/c', then the two straight lines are happening together, and hence would intersect each other on a countless number of points. Algebra calls it an infinitely many solutions' case.

And you are talking about the third case here...
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by gmat_perfect » Sat Mar 27, 2010 11:02 pm
Thanks for reply.

So, what is the conclusion?

If two lines have same slope, they can interesect.

Any comment?

Thanks.
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by gmat_perfect » Mon Mar 29, 2010 12:13 am
comment lease.
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by harshavardhanc » Mon Mar 29, 2010 2:38 am
gmat_perfect wrote:comment lease.
two lines with same slope :

Case 1 : parallel -----------------------> never intersect

Case 2 : two representations of the same line. One over the other. Always intersect.
Regards,
Harsha
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