Find the slope of the line passing through each of the following pairs of points. (−3, 9), (−3, −5) (5, 6), (3, 4) (0, 7), (0, −8) (4, 0), (−2, 8)

Look carefully at the first pair:  (−3, 9), (−3, −5)  Note that x does not change, tho' y does.  This is how we recognize a vertical line (whose slope is undefined).  The equation of this vertical line is x = -3.

Looking at the second pair:  from (3,4) to (5,6), x increases by 2 and y by 2; thus, the slope is m = rise/run = 2/2 = 1.

Third pair:  as was the case with the first pair, x does not change here, and thus the equation of this (vertical) line is x=0 (which is the y-axis).  The slope is undefined.