Explain how slope is used to determine if a triangle is a right triangle.

Do determine if a triangle is a right triangle using slopes, you have to understand perpendicular slopes/negative reciprocals. 

You can calculate the slope of all 3 sides of the triangle and if two of the slopes are negative reciprocals, then those two lines intersect creating a right angle/right triangle. 

Let's say there's triangle ABC. 

If the slope of AB is 1/2
and the slope of BC is 2/5
and the slope of CA is -2/1
then AB and CA intersect resulting in a right angle (triangle).