5.4 slope as a rate of change complete lesson.notebook
TRANSCRIPT
5.4 Slope as a Rate of Change complete lesson.notebook1
I will be able to... ...calculate the rate of change
in different scenarios
**Quiz Tomorrow!
A Runner's Run
2
Feb 911:33 AM
• a change in one quantity relative to the change in another quantity • calculated the same way as slope, but the answer must include units
Feb 911:43 AM
3
4
5
I will be able to... ...calculate the rate of change
in different scenarios Practice Questions:
I will complete... pg. 268 #17, 1214 **Quiz Tomorrow!
Nov 38:00 AM
6
7
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.
Give one reason why some homes have roofs which have a greater pitch.
There is less snow build up in the wintertime.
Engineers refer to the slope of a road as the grade.
They often refer to the slope as a percentage.
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
run of 100 units, there is a rise of 8 units.
= 8%
The steepness of wheelchair ramps is of great importance to handicapped persons.
The slope of wheelchair ramps is usually about
1
12
If the rise is 1.5 m, what is the run?
Ans: 18 m
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.
3 m
5 m
Determine the slope of the staircase.
2
3
3
3
2
4
6
10
8
0
12
14
4
6
8
10
12
2
3
9
Confirm with the class that other points on the line besides (4,6) and (13,9) would also have given slope 1/3.
Determine the slope.
2
4
6
10
8
0
12
14
4
6
8
10
12
2
– 5
7
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.
Horizontal lines have a slope of zero.
2
4
6
10
8
0
12
14
4
6
8
10
12
2
7
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.
Vertical lines have slopes which are undefined.
2
4
6
10
8
0
12
14
4
6
8
10
12
2
6
The rise between the green points is 6, but, this time, the run is 0.
Summary: Types of Slopes
Which points will you use to determine rise and run?
5
40
= 8
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
60
–2
Draw a line which has a slope of 2
Draw a line which has a slope of
–5
6
–5
6
–3
1
–3
1
I will be able to... ...calculate the rate of change
in different scenarios
**Quiz Tomorrow!
A Runner's Run
2
Feb 911:33 AM
• a change in one quantity relative to the change in another quantity • calculated the same way as slope, but the answer must include units
Feb 911:43 AM
3
4
5
I will be able to... ...calculate the rate of change
in different scenarios Practice Questions:
I will complete... pg. 268 #17, 1214 **Quiz Tomorrow!
Nov 38:00 AM
6
7
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.
Give one reason why some homes have roofs which have a greater pitch.
There is less snow build up in the wintertime.
Engineers refer to the slope of a road as the grade.
They often refer to the slope as a percentage.
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
run of 100 units, there is a rise of 8 units.
= 8%
The steepness of wheelchair ramps is of great importance to handicapped persons.
The slope of wheelchair ramps is usually about
1
12
If the rise is 1.5 m, what is the run?
Ans: 18 m
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.
3 m
5 m
Determine the slope of the staircase.
2
3
3
3
2
4
6
10
8
0
12
14
4
6
8
10
12
2
3
9
Confirm with the class that other points on the line besides (4,6) and (13,9) would also have given slope 1/3.
Determine the slope.
2
4
6
10
8
0
12
14
4
6
8
10
12
2
– 5
7
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.
Horizontal lines have a slope of zero.
2
4
6
10
8
0
12
14
4
6
8
10
12
2
7
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.
Vertical lines have slopes which are undefined.
2
4
6
10
8
0
12
14
4
6
8
10
12
2
6
The rise between the green points is 6, but, this time, the run is 0.
Summary: Types of Slopes
Which points will you use to determine rise and run?
5
40
= 8
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
60
–2
Draw a line which has a slope of 2
Draw a line which has a slope of
–5
6
–5
6
–3
1
–3
1