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

Question

mateusrhodes · Answer

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$$y = ax$$

anonymous · Answer

Is b the y-intercept?

mateusrhodes · Answer

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