Suppose the graph of a line has a negative slope and a positive y-intercept. through which quadrants does the line pass?

A negative slope means the line tilts down to the right and up to the left.
Since it has a positive y-intercept, it must go up to the left of the y-axis.
That means it must be in quadrant 2. Then as it crosses the y-axis, it must go into quadrant 1. Given enough length, it will have to go into quadrant 4 also.
The answer is: Quadrants 1, 2, 4