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![Page 1: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/1.jpg)
4-1A Rate of Change and the Slope of a Line Using a Graph
Algebra 1 Glencoe McGraw-Hill Linda Stamper
![Page 2: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/2.jpg)
Rate of change is a ratio that describes, on average, how much one quantity changes with respect to a change in another quantity. If x is the independent variable and y is the dependent variable, then
xx yy
1 6
2 12
3 18
4 24
xinchangeyinchange
changeofrate +6
+6
+6
6
+
1 +
1 +
1
16
The rate of change is 6.
![Page 3: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/3.jpg)
Example 1 Use the table to find the rate of change.
xx yy
2 6
4 12
6 18
8 24
xinchangeyinchange
changeofrate +6
+6
+6
6
+
2 +
2 +
2
2
3
The rate of change is 3.
![Page 4: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/4.jpg)
You have been graphing linear equations which graph as a line.
In this lesson you will learn about slope.
1isslope
Slope is the steepness of a line.
![Page 5: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/5.jpg)
You have been graphing linear equations which graph as a line.
In this lesson you will learn about slope.
Slope is the steepness of a line.
2isslope
![Page 6: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/6.jpg)
You have been graphing linear equations which graph as a line.
In this lesson you will learn about slope.
run horizontal
rise vertical slope Slope is a ratio of rise to run.
31
isslope
Slope is the steepness of a line.
![Page 7: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/7.jpg)
Find the slope of a hill that has a vertical rise of 40 feet and a horizontal run of 200 feet. Let m represent slope.
Write word ratio.runrise
m
Substitute.20040
Simplify – write in lowest terms. 51
![Page 8: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/8.jpg)
Example 2 Find the slope of a wheelchair ramp that has a vertical rise of 2 feet and a horizontal run of 24 feet. Let m represent slope.
runrise
m
242
121
Example 3 Find the slope of a ski trail that has a vertical rise of -3 feet and a horizontal run of 4 feet. Let m represent slope.
runrise
m
34
43
![Page 9: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/9.jpg)
Types of SlopeImagine that you are walking to the right on a
line.A positive slope means that you are walking uphill.
![Page 10: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/10.jpg)
Imagine that you are walking to the right on a line.A negative slope means that you are walking downhill.
Types of Slope
![Page 11: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/11.jpg)
Imagine that you are walking to the right on a line. Zero slope means that you are walking on level ground.
Do not identify this as “no slope”.
Types of Slope
![Page 12: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/12.jpg)
Undefined slope is a vertical line. You can not walk up a vertical line. It is not possible. You would fall!
Do not identify this as “no slope”.
ouch!
Types of Slope
![Page 13: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/13.jpg)
zero
Types of Slope are words!
positive
negative
undefined
![Page 14: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/14.jpg)
Find the Slope by Walking the Line
This means to calculate the slope - to
find the steepness of the line!
![Page 15: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/15.jpg)
Find the Slope by Walking the LineWhen you find the slope by
walking the line, moving upward on the graph is positive. Moving left on the graph is negative.
Moving right on the graph is positive.
x
y
•
•Moving downward on the graph is negative.
![Page 16: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/16.jpg)
Find the slope of the line.
Start at either point. Find the vertical rise. Up is positive and down is negative.
4
Find the horizontal run. Going right is positive and going left is negative.
2
Simplify.
2x
y
•
•
runrise
mWrite slope ratio.Write slope ratio. MANDATORY STEP
![Page 17: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/17.jpg)
Find the slope of the line.
Start at either point. Find the vertical rise. Up is positive and down is negative.
4
Find the horizontal run. Going right is positive and going left is negative.
2
Simplify.
2x
y
•
•
runrise
mWrite slope ratio.
•
••
Slope is the rate of change. It will change -2 all along the line.
![Page 18: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/18.jpg)
Example 4A Find the slope of the line.
2. Start at either point. Find the vertical rise. Up is positive and down is negative.
4
3. Find the horizontal run. Going right is positive and going left is negative.
74
It does not matter at which point you begin the walk!
x
y1. Write slope ratio.runrise
m
•
•
![Page 19: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/19.jpg)
Example 4B Find the slope of the line.
2. Start at either point. Find the vertical rise. Up is positive and down is negative.
4
3. Find the horizontal run. Going right is positive and going left is negative.
74
It does not matter at which point you begin the walk!
x
y1. Write slope ratio.runrise
m
•
•7
![Page 20: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/20.jpg)
Example 5 Find the slope of the line.
2. Start at either point. Find the vertical rise. Up is positive and down is negative.
0
3. Find the horizontal run. Going right is positive and going left is negative.
5
4. Simplify
0
x
y1. Write slope ratio.
runrise
m
• •
zero ooooover the fraction line
is (zeroooooo)
![Page 21: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/21.jpg)
Example 6 Find the slope of the line.
2. Start at either point. Find the vertical rise. Up is positive and down is negative.
4
3. Find the horizontal run. Going right is positive and going left is negative.
0
4. Simplify
undefined
x
y
1. Write slope ratio.
runrise
m
zero unnnnder the fraction line
is unnnnndefine
d
•
•
![Page 22: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/22.jpg)
PRACTICE. Plot the points and draw the line that passes through them. Then find the slope using the slope ratio.1. (2,4) and (2,-4) 3. (3,6) and (3,–1) 5. (6,1) and
(–4,1)2. (4,5) and (2,2) 4. (-2,-3) and (3,-3) 6. (2,2) and
(–1,4)Find the slope by walking the line.
7.•
•
8.
••
x
y
x
yWriting the
slope ratio is a mandatory
step!
![Page 23: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/23.jpg)
PRACTICE. Answers
1. (2,4) and (2,-4) 4. (-2,-3) and (3,-3)2. (4,5) and (2,2) 5. (6,1) and (–4,1)3. (3,6) and (3,–1) 6. (2,2) and (–1,4)
7.•
•
8.
••
x
y
x
y
2 52
undefined 0
23
0
32undefined
![Page 24: 4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649de85503460f94ae1e44/html5/thumbnails/24.jpg)
4-A2 SKILLS PRACTICE Wkbk. Page 24 #1–19
#4 – 19 Plot the points and draw the line that passes through them. Then find the slope using the slope ratio. Skip #12.