To understand how slopes help us figure out how a triangle is positioned on a graph, let's break it down into simpler parts.

1. What is Slope?
   Slope tells us how steep a line is, and it connects two points on a graph. We can find the slope using this formula:
   [ m = \frac{y_2 - y_1}{x_2 - x_1} ]
   This means we look at how much the line goes up or down compared to how much it goes across. If the slope is positive, the line goes up, and if it’s negative, the line goes down.

2. How Does Slope Show Triangle Orientation?
   By looking at the slopes of a triangle's sides, we can tell if the triangle is standing straight, leaning, or flipped upside down. For example:

   • If all three slopes are positive, the triangle might point to the right.
   • If two sides have positive slopes and one side has a negative slope, then the triangle leans to one side.

3. Why Does This Matter?
   Knowing the slopes helps us identify different types of triangles, like right triangles or isosceles triangles, based on how their angles are positioned. So, by analyzing slopes, we can learn more about the triangle's shape and position on the graph!