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

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

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

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

7. 8 100 A grade of 8% would mean for every run of 100 units, there is a rise of 8 units. = 8%

8. Determine the slope of the line. 5 cm 9 cm We use the letter m because in French the word for “to go up” is monter. Because the slope is a ratio, there are no units such as cm or cm 2.

9. 3 m 5 m Determine the slope (pitch) of the roof.

10. Determine the slope of the staircase. 2 3 3 3

11. 3 9 2 4 6 10 8 0 12 14 4 6 8 10 12 2 Determine the slope.

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

13. 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.

14. 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.

15. positive negative zero undefined Summary: Types of Slopes

16. Note! The steeper the line, the greater the slope! Positive & Negative Slopes Always look at the graph from LEFT to RIGHT. If the line is moving upward, then the graph is increasing and the slope is positive. If the line is moving downward, then the graph is decreasing and the slope is negative. Positive Slope Negative Slope

17. Determine the slope of this line. Which points will you use to determine rise and run? 5 40 = 8

18. Determine the slope of the line segment. 60 –2

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

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

21. Draw a line which has a slope of … –3 1 1 a) – 3 b) 3 3 1 3 1

22. Rise = - 3 Run = 1 A line segment has one endpoint, A(4,7), and a slope of -3. Find the coordinates of another possible endpoint, B. m = - 3 1 A slope of -3 is the same as: Thus, starting from our original point of A(4,7) we can move DOWN 3 units and to the RIGHT 1 unit to find another point on the line. Thus, another possible endpoint is B(5,4)

23. Directions PositiveNegative Rise Run

24. Page 259 #2, 3, 5, 8, 9, 11, 12b,13, 16