The vertices of a parallelogram are j (-5,0) k(1,4), l(3,1) and m(-3,-3). how can you use slope to determine whether the parallelogram is a rectangle? is it a rectangle? justify your answer.

You have to check the slopes of two sides that intersect each other to see if the slopes are negative reciprocals of each other, which proves perpendicular for a rectangle to exist.  If not perpendicular, then it is a parallelogram only.

These turn out to be slopes of 2/3 and -3/2 for perpendicular,
and the same of another pair of slopes.
So the figure is a rectangle.