Why did it pass from (1,-2) and ((-1,0). I understood that b= -1 that makes (0,-1) and m= -1 that could be -1/1 or 1/-1.

m= rise/run

so if m= -1/1 shouldn’t it pass through (-1,1) and then for m=1/-1 shouldn’t it pass through (1,-1). I am confused.

Slope and coordinates are different. When you say slope is 1/-1 or -1/1, what you mean is the difference of y coordinates over the difference of x coordinates (what you termed as rise and run). i.e. \frac{y2-y1}{x2-x1} and not the coordinates themselves.

So the slope gives no information by itself about what coordinates the line passes through. In the following graph, it is clear that all the lines have a slope of -1, but all of them pass through different coordinates.

In the given problem, since you are clear that the line passes through (0,-1) you can assume that x1 = 0, y1 = -1. Now to find where it passes the x axis, we know that the y coordinate of such a point will be 0, so x2= unknown, y2 = 0. Since you know that the slope is -1 try equating all values to m = \frac{y2-y1}{x2-x1} and find what you’ll simplify x2 to be. So now that (x2, y2) will be the coordinate of what point the line passes through

How did Greg get those coordinates (-1,0) and (1,-2). Do I start looking rise and run from (0,-1) which is the y intercept coordinate?

I’m not familiar with the context of the question. Can you please repost the question here?