Question

1. why are there infinite lines parallel to y = mx + b for any slope?

Explanation:

Parallel lines have the same slope. The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. Since \(b\) can take on an infinite number of values (any real number), there are an infinite number of lines with the same slope \(m\) (parallel to \(y=mx + b\)).

Answer:

Because the \(y\) - intercept (\(b\)) in the line equation \(y = mx + b\) can be any real number, and for each different value of \(b\) (while keeping \(m\) the same), we get a different line parallel to \(y = mx + b\).