Question

Does every line have an infinite number of lines that are parallel to the given line? Explain.

Answer 1

Yes.
For instance,let there be a line on the xy plane,\[y = ax,a \in \mathbb{R}\]
Let there be another arbitrary line\[y = a(x-b),b \in \mathbb{R}\]
This line has the same slope,but it is moved along the x axis by b units.
Since b can assume an infinite number of values,and for each b we can associate with a line,there is an infinite number of parallel lines to\[y = ax\]

Answer 2

Is b the y-intercept?

Answer 3

In this case, -ab is the y- intercept ,by taking x =0