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. REFLECTION: Why might some homes have roofs with a greater pitch?
ANSWER: There is less snow build up in the wintertime.

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

5. When talking about the grade of a road, they often refer to the slope as a percentage.

6. The slope of a line is the steepness of the line.
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 rise of 8 units, there is a run of 100 units.
= 8%

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

9. EX. 1. 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. EX. 2. Determine the slope (pitch) of the roof.

11. EX. 3. Determine the slope of the staircases.
RED:
BLUE: 2 3 3 3

12. EX. 4. 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. EX. 5. Determine the slope. – 5 7 12 10 8 6 4 2 4 6 8 2 10 12 14
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. Horizontal lines have a slope of zero.
EX. 6. Determine the slope. 12 10 7 8 6 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. Vertical lines have slopes which are undefined.
EX. 7. Determine the slope. 12 6 10 8 6 4
The rise between the green points is 6, but, this time, the run is 0.
Vertical lines have slopes which are undefined. 2 2 4 6 8 10 12 14

16. Summary: Types of Slopes
positive
negative
undefined
zero

17. = 8 EX. 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. EX. 9. Determine the slope of the line segment.–2 60

19. EX. 10. Draw a line which has a slope of

20. EX. 12. Draw a line which has a slope of–5 6 –5 6

21. EX. 13. Draw a line which has a slope of …
b) 3 1 –3 3 1 1 –3 3 1