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".

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...

Thanks for reply.

So, what is the conclusion?

If two lines have same slope, they can interesect.

Any comment?

Thanks.

comment lease.

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.