Graphing & Analytic Geometry MPM1DI Unit 4 Graphing & Analytic Geometry Day 3: Slope Learning Goal: Students can determine the slope of the line.

Slopes (or steepness) of lines are seen everywhere.

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

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

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

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

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.

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

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.

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

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

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

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

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

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

Summary: Types of Slopes positive negative undefined zero

= 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

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

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

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

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