Note: This is the third part of the Slope Concept Series.

Part I: Basic Understanding of Slope

Part II: Slope of the Graph of a Linear Function

In the Understanding the Basic Concepts of Slope post, we have discussed that the slope of a line in the coordinate plane is described as the *change in y *over the *change in* *x*. When we say *change in x,* or *change in y*, we talk about the ‘change distance.’ To determine a distance we need two points. If we are in the coordinate plane, and we have two points with coordinates and , then the rise is and the run is . Thus, the slope of the line containing the two points is .

We also have discussed that the slope of a horizontal line is 0 by rotation. Here, we will show the same fact using coordinates as shown.

A horizontal line has the same *y*-coordinates everywhere. Let us consider line *l* in Figure 2 with equation . Let us pick two points with coordinates and . Using the formula above, calculating for the slope we have . Hence, the slope of a horizontal line *l* is .

Similarly, a vertical line has the same *x*-coordinate everywhere. Let us consider line *m* in Figure 3 with equation . Let us pick two points with coordinates and . Using the formula above, calculating the slope, we have which is undefined.

In the sequel of this post, we will discuss the lines with positive and negative slopes.