1. Slope The slope of a line can be thought of as a measure of the steepness of the line. A horizontal line isn’t steep at all, and has a slope of zero.

2. The slope of a line rising on an angle of 45 degrees is positive one.

3. The slope of a line falling on an angle of 45 degrees is negative one.

4. Here is a line that is rising, but not very steep. Rising indicates a positive slope … … and not very steep (less than 45 degrees) suggests a slope of less than one.

5. Here is a line that is rising, and is steep. Rising indicates a positive slope … … and steep (greater than 45 degrees) suggests a slope of more than one.

6. The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line. The letter m is often used to represent slope. Let’s be a bit more precise, rather than using the concept of “steepness”.

7. Find two points on the line … Example 1: Consider the following graph.

9. There are a variety of ways for describing slope: SLOPE GeometricAlgebraic

10. Example 2: Find the slope of the line that contains the points (- 5, 3) and (4, 0).

11. Geometric Interpretation of slope: In example 2, means the line falls 1 unit (because of the negative) for every three units to the right as shown by the red arrows on the graph.

12. Example 3: which is undefined. Find the slope of the line that contains the points (- 1, 3) and (- 1, - 2).

13. In example three, the slope was found to be undefined. Here the two points lie on a vertical line. The slope of a vertical line is undefined. The slope of a horizontal line is zero. Facts About Special Lines