Question

How to find a slope of a line parallel to the graph of each equation `y=-2/3x - 1`?

Answer 1

The answer is already written! :)

You'll agree that two lines are parallel if the have the same slope. But if you write a line's equation in the form `y=mx+q`, then `m` is exactly the slope of the line. So, in your case, the slope is `-2/3`. So, every other line with slope `-2/3` is parallel to your line.

In other words, you can change the `q` coefficient as you like, obtaining (all) infinite other lines parallel to yours.

This make sense, since changing the `q` coefficient only translates the line upwards or downwards. This is exactly how you obtain parallel lines to a given one: you take it and you shift it a little bit! :)