Question

There is only one line that can be parallel to a given line. T/F

Answer 1

I believe it is false.

Answer 2

why do you think false?

Answer 3

Since I thought that if lines are next to each other (parallel), no matter how many there are they are all parallel.

Answer 4

That's one way to think of it. Another is to list a specific counter-example to prove the claim to be false

So let's say we have the line y = x

The line y = x+1 is parallel to that, but so is y = x+2, y = x+3, etc etc

All of these lines have a slope of 1 which is why they are parallel

Answer 5

Ahh I see. Thank you very much for giving me an explanation!

Answer 6

you're welcome