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

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

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

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. 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

9. 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 cm2.

10. Determine the slope (pitch) of the roof.

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

12. Determine the slope. 12 10 9 3 8 6 4
Confirm with the class that other points on the line besides (4,6) and (13,9) would also have given slope 1/3. 2 2 4 6 8 10 12 14

13. Determine the slope. 12 10
– 5 8 6 7 4
A student may ask about the possibility of seeing the upward/positive rise from (11,5) to (4,10) as 5. Confirm that this is correct, but would generate a negative/leftward run of –7 and yield the same negative slope. 2 4 6 8 2 10 12 14

14. Determine the slope. 7 Horizontal lines have a slope of zero. 12 10 86 4
The run between the green points is 7. The line does not rise between the green points, so rise =0.
No matter what two points are chosen on the red line, rise will be 0 and run will be positive (rightward) or negative (leftward). Since 0/+=0 and 0/-=0, the slope will 0. 2
Horizontal lines have a slope of zero. 2 4 6 8 10 12 14

15. Determine the slope. 6 Vertical lines have slopes which are undefined.12 6 10 8 6 4
Vertical lines have slopes which are undefined.
The rise between the green points is 6, but, this time, the run is 0. 2 2 4 6 8 10 12 14

16. Summary: Types of Slopes
positive
negative
undefined
zero

17. = 8 Determine the slope of this line.
Which points will you use to determine rise and run? 40 5
M=rise/run
To measure rise and run, we could count squares between 2 points on the line. From the graph it is easy to read the coordinates of (2,30) and (7,70) since these fall on grid lines.
Mark these 2 points and use the given scales to measure rise and run.
Rise =40
Run=5
M=40/5
M=8
= 8

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

19. Draw a line which has a slope of

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

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