Answer:
Infinity (the line would be vertical and thus the slope would be undefined)
Explanation:
First, find the equation of the line connecting (-2, -2) and (-2, -3). Notice that x does not change here, while y does change. Thus, the line through these two points is a vertical one. Any line that is perpendicular to this vertical line x = -2 and situated between the given points will never touch the points.
The answer to this question is: One possible value for the slope of a line passing between the given points but not containing either one of them is "undefined." Actually, this is the ONLY possible value of the slope of this line thru (1,1) could have if you want a 100% guarantee that this line does not contain either (-2, -2) or (-2, -3).