Question 62667
First find the slope of the given line through (-3,5) and (4,-6)

The slope = difference in y co-ordinates/ difference in x co-ordinates

         = (-6-5)/(4-(-3))

         = -11/(4+3)

         = -11/7

The slope of the line perpendicular to this line is given by:

slope = -1/slope of the given line  [As product of the slopes of perpendicular 

                                     lines = -1]

       = (-1)/ (-11/7)

       = (-1)*(7/-11)

       = 7/11

Required slope = 7/11

Good Luck!!!