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

Yes

Step-by-step explanation:

If you have a line, for example:

where  is the slope and is the point where that line crosses the y axis calles the y-intercept.

And another line parallel to the first line:

the slopes of both lines must meet the following condition

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 can have any value (an infinite number of values)

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

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