Could you please explain question 8 of test #4 section 4 of the blue book?

Sure. It’s really helpful to see this one represented visually. The question says that the line in question goes through parts of quadrants II, III, and IV. That means it goes through each of the non-gray quadrants below.

The only way a line can be in all three quadrants is if it has a negative slope, like the lines sketched on the figure below.

Undefined slope means a vertical line, so that can’t be in three quadrants. Slope of 0 means a horizontal line; that can’t be in three quadrants, either. And try as you might, you can’t draw a line with a positive slope that doesn’t eventually get into quadrant I.

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