How do you determine the slope of #(3, –5)# and #(–2, 9)#?
I suppose you want the slope of the line joining the two points. If it is so the answer should be -14/5.
Consider that the slope represents the rate of change of y with x. In other words, if you have a slope of, say, 5 this means that every change of 1 units in x (let say from 6 to 7) implies a change of 5 in y (let say from 6 to 11):
so, slope is: (change in y) / (change in x)
in your case you have
when x goes from -2 to 3 it increases of 5 units while y goes from 9 to -5 DECREASING of 14 units and so giving a NEGATIVE slope of -14/5.