The student will learn to find the slope of a line given two points on a graph or explicitly given the points. Slope is defined as the steepness or rise over run of a line between two points. You can find the slope by taking the difference in the y-values and dividing by the difference in the x-values of the two points. Slope can be positive, negative, zero if horizontal, or undefined if vertical. Examples are worked through of finding the slope given two points on a graph or the points explicitly.

1. Objective The student will be able to: find the slope of a line given 2 points and a graph.

2. Introduction To Slope

3. What is the meaning of this sign? Icy Road Ahead Steep Road Ahead Curvy Road Ahead Trucks Entering Highway Ahead

4. What does the 7% mean? 7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally. So, what is slope??? Slope is the steepness of a line. 7% 7 feet 100 feet

5. Finding Slope Given a Graph

6. When given the graph, it is easier to apply “ rise over run ”. 1) Determine the slope of the line.

7. Determine the slope of the line. Start with the lower point and count how much you rise and run to get to the other point! 6 3 run 3 6 = = rise Notice the slope is positive AND the line increases!

8. Determine the slope of the line. The line is decreasing (slope is negative). 2 -1 Find points on the graph. Use two of them and apply rise over run.

9. What is the slope of a horizontal line?

10. What is the slope of a vertical line?

11. Remember the word “VUXHOY” V ertical lines U ndefined slope X = number; This is the equation of the line. H orizontal lines O - zero is the slope Y = number; This is the equation of the line.

12. Types of Slope Positive Negative Zero Undefined or No Slope

13. Dude! You try one.

14. Determine the slope of the line shown. -2 -½ ½ 2

15. rise = 4 run = 5 m= rise run m= 4/5

16. Finding Slope Given 2 points

17. Find the slope of the line through the points (3,7) and (5, 19). x 1 y 1 x 2 y 2 m = 19 – 7 5 – 3 m = 12 2 m = 6

18. Find the slope of the line that passes through the points (-2, -2) and (4, 1). y 2 = 1 x 2 = 4 y 1 = -2 x 1 = -2

19. Find the slope of the line that goes through the points (-5, 3) and (2, 1).

20. The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula

21. To solve for r, simplify and write as a proportion. Cross multiply. 1(-4) = 4(4 – r)

22. Simplify and solve the equation. 1(-4) = 4(4 – r) -4 = 16 – 4r -16 -16 -20 = -4r -4 -4 5 = r The ordered pairs are (5, 6) and (4, 2)

23. Dude! You try one.

24. Find the slope of the line that passes through (3, 5) and (-1, 4). 4 -4 ¼ - ¼

25. The End