Question

Does every line have an infinite number of lines that are parallel to it

Answer 1

Yes. Every line has an infinite number of lines that are parallel to it. I do believe this is true since each plane extends forever in every direction.

Answer 2

Yes

Explanation:

If you have a line, for example:

`y=m_(1)x+b_(1)`

where
`m_(1)` is the slope and
`b_(1)` is the point where that line crosses the y axis calles the y-intercept.

And another line parallel to the first line:

`y=m_(2)x+b_(2)`

the slopes of both lines must meet the following condition

`m_(1)*m_(2)=-1`

so as we can see we have a condition for the slope of a parallel line, but we dont have a condition or restriction for the y-intercept of the parallel line, so
`b_(2)` can have any value (an infinite number of values)

which means that there are an infinite number of parallel lines for any straight line.