Use the slopes of the sides of the triangle to prove that the triangle is a right triangle. show all of your work for full credit.

I have added the diagram of the question.

To prove that the triangle is right, we need to prove that there is a right-angle in it. This means that we need to prove that there are two perpendicular sides.

If two lines are perpendicular:
slope of first line = -1 / slope of second line

If two lines are parallel:
slope of first line = slope of second line

Now, for the given:
1- slope of the base:
slope = 

The slope of this line is zero (line parallel to x-axis)

2- slope of the height:
slope = 

The slope of this line is undefined (line parallel to y-axis)

By definition, we know that the x-axis is perpendicular to the y-axis.
Since the base is parallel to the x-axis and the height is parallel to the y-axis, therefore, the base and the height are perpendicular.

This means that the triangle is a right-angled triangle

Hope this helps :)