1. Slopes
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What is 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. Malibu House

5. Ranch House

6. Ski Cabin

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

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

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

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

12. Slopes and Lines
rise
run

13. 8
100
A grade of 8% would mean that for every run of 100 units, there is a rise of 8 units.

14. The steepness of wheelchair ramps is of great importance to handicapped persons.1 12
The slope of wheelchair ramps is usually about
If the rise is 1.5 m, what is the run?
Ans: 18 m

15. Determine the slope of the line segment.
9 cm
5 cm
We use the letter m because in French the word for “to go up” is monter.
René Descartes ( ) was from France and he was the first to define the Cartesian Plane.

16. Determine the slope (pitch) of the roof.
Because the slope is a ratio, there are no units such as cm or cm2.

17. SLOPE

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

22. Determine the slope of the line segment.y 7 4 x

23. Determine the slope of the line segment.y –5 7 x

24. Determine the slope of the line segment.y 6
Horizontal lines have a slope of zero. x

25. Determine the slope of the line segment.y 5
Vertical lines have slopes which are undefined. x

26. negative
positive
undefined
zero

27. Determine the slope of the line segmenty 5 40
= 8 x

28. Determine the slope of the line segmenty –2 60 x

29. Draw a line which has a slope of

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

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

32. Find the slope of the line through (2,1) and (5,3)

33. Wouldn’t it be convenient if we could find the slope of a line without having to plot the points? We can if we use the slope formula .
Slope Formula:

34. Use the slope formula to find the slope of the line through (2,1) and (5,3)

35. Use the slope formula to find the slope of the following line segments:
1) A (2, 4) to B (6, 7)
2) C (-3, 4) to D (1,-2)
3) E (-1,-4) to F (7,-8)