1. Finding the Slope

2. The Question Given the two point (-3,1) and (3,3) which lie on a line, determine the slope of that line. First, let’s draw the graph, so that we may use slope = to develop a new formula.

3. Graph the Line

4. Finding Slope Using Rise & Run Rise Run = 3 – 1 = 2 = 3 – (-3) = 6

5. Finding the Slope m =

6. Finding Slope Another Way Now, recall that rise is the vertical change (or the difference between y-coordinates) and run is the horizontal change (or the difference between x-coordinates)

7. Finding Slope Another Way The first point is (-3,1) is thought of as (x 1,y 1 ) and the second point (3,3) is thought of as (x 2,y 2 ). (-3,1) (3,3)

8. Finding Slope Another Way Now,m = m = But, rise is the change in the y coordinates,  y And, run is the change in the x coordinates,  x

9. Finding the Slope Another Way m = Therefore, we get the same answer using both methods.

10. Formula for Slope Thus, we can find the slope using m = Or we can find the slope using m = And we come up with the same answer. You can choose which method works best depending of if you have the graph or just the coordinates of the points.