1. The Slope of a Line

2. Finding Slope of a Line The method for finding the steepness of stairs suggests a way to find the steepness of a line. A line drawn from the bottom step to the top set of a set of stairs touches each step in one point. The rise and the run of a step are the vertical and the horizontal changes, respectively, between two points on the line.

3. Finding the Slope of a Line The steepness of the line is the ratio of rise to run, or vertical change to horizontal change, for this step. We call the steepness of a line its slope.

4. Important things about slope… Slope is the change in y over change in x. Slope is represented by the letter m Vertical line has NO slope ( undefined ) Horizontal line has a slope zero (0)

5. Formula for slope:

6. Find the slope of a line passing through points (-2,4) and (3,6) m = 6 - 4 3 - - 2 = 2 5 m = 4 - 6 -2 - 3 = -2 -5 2 5 = or

7. Find the slope of a line passing through points (1,1) and (3,-2) = - 3 2

8. A slope of - 3 / 2 means that or every time y goes down 3, x moves over 2 Graph and count to check.

9. Classify lines by their slope: 1. A line with a positive slope rises from left to right (m>0) x y

10. 2. A line with a negative slope falls down from left to right (m<0) x y

11. 3. A line with a zero slope is horizontal (m=0) Equation y = 3 x y

12. 4. A line with an undefined slope is vertical (m is undefined) YOU CANT DIVIDE BY 0! x y

13. Find the slope by using the graph. 1 2 3 4 -4 -3 -2 -4-3-2 1234 To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary. This line goes up 2 and over 1. The slope is 2 / 1 or 2.

14. Find the slope by using the graph. 1 2 3 4 -4 -3 -2 -4-3-2 1234 To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary. This line goes down 2 and over 1. The slope is - 2 / 1 or -2.