1. Slope

2. Slopes (or steepness) of lines are seen everywhere.

3. The steepness of the roof of a house is referred to as the pitch of the roof by home builders.

4. Give one reason why some homes have roofs which have a greater pitch. There is less snow build up in the wintertime.

5. Engineers refer to the slope of a road as the grade.

6. They often refer to the slope as a percentage.

7. Slopes and Lines rise run The slope of a line is the steepness of the line.

8. 8 ft 100 ft A grade of 8% would mean for every rise of 8 feet, there is a run of 100 feet. = 8%

9. The steepness of wheelchair ramps is of great importance to those who use them. The slope of wheelchair ramps is usually about 1 foot rise for every 12 feet of run. 1 ft 12 ft If the rise is 2 feet, what is the run? Answer: 24 feet

10. 3 m 5 m Determine the slope (pitch) of the roof. mmmm

11. Determine the slope of the staircase. 2 3 3 3 = 1

12. 6 yd 3 sec 2 4 6 10801214 4 6 8 10 12 2 Determine the slope. Distance (yards) Time (seconds) m = 6 yards 3 seconds m = 2 yds/sec

13. – 5 7 Determine the slope. 2 4 6 10 8 0 12 14 4 6 8 10 12 2

14. 7 Horizontal lines have a slope of zero. 2 4 6 10 8 0 12 14 4 6 8 10 12 2 Determine the slope.

15. 6 Vertical lines have slopes which are undefined. 2 4 6 10 8 0 12 14 4 6 8 10 12 2 Determine the slope. cannot divide by zero!

16. positive negative zero undefined Summary: Types of Slopes

17. Slope Mountain Ski Resort Positive slope, + work Negative slope, - work Zero slope is zero fun! Undefined slope. Oh No!!!! T. Merrill 2005

18. Slope of line through 2 points To find the slope of a line through 2 given points we use the formula For example, Find the slope of a line that goes through (-3, 5) and (2, 18) x1x1 y1y1 x2x2 y2y2 18 5 2 -3

19. Determine the slope of this line. 5 40 = 8 How can you find slope when counting lines is just too much?

20. Let’s take a closer look... (7, 70) (2, 30) ΔxΔx ΔyΔy

21. In general, (x 2, y 2 ) (x 1, y 1 ) ΔxΔx ΔyΔy

22. Determine the slope of the line segment. (20, 7) (80, 5) x 1 y 1 x 2 y 2

23. Draw a line which has a slope of Draw a line which has a slope of 2

24. Draw a line which has a slope of –5 6 6

25. What Type of Slope is Shown? Positive Slope Negative Slope Zero Slope No Slope/Undefined

26. Slope of a Table In a table we can use the same formula. Pick any two pairs in the table for coordinates xy -4-17 1-2 34 819 1025 Pick any two rows. If it is linear it will be the same no matter which two rows you pick x1x1 x2x2 y1y1 y2y2

27. Conclusion Slope is: Describe the slope of each of the following the rate of change of a line Negative slope Undefined/ No slope Positive slope Zero/0 slope