4-1A Rate of Change and the Slope of a Line Using a Graph

1
4-1A Rate of Change and the Slope of a Line
Using a Graph
Homework Alert 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)
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
2
What is the standard form for a linear equation?
Ax By C
The x-intercept and the y-intercept are numerical
values. They are NOT __________. They are NOT
_______.
equations!
ordered pairs!
3
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
x y
1 6
2 12
3 18
4 24
4
1
4
1
4
1
The rate of change is 4.
4
Example 1 Use the table to find the rate of
change.
x y
2 6
4 12
6 18
8 24
6
2
6
2
6
2
The rate of change is 3.
5
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.










6
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.










7
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.
Slope is a ratio of rise to run.










8
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.
Substitute.
Simplify write in lowest terms.










9
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.
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.




















10
Types of Slope
Imagine that you are walking to the right on a
line.
A positive slope means that you are walking
uphill.










11
Types of Slope
Imagine that you are walking to the right on a
line.
A negative slope means that you are walking
downhill.










12
Types of Slope
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.
13
Types of Slope
Undefined slope is a vertical line. You can not
walk up a vertical line. It is not possible. You
would fall!










ouch!
Do not identify this as no slope.
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Types of Slope are words!
positive
negative
zero
undefined










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Find the Slope by Walking the Line
This means to calculate the slope - to find the
steepness of the line!
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Find the Slope by Walking the Line
When you find the slope by walking the line,
moving upward on the graph is positive.
y










Moving left on the graph is negative.

x
Moving downward on the graph is negative.

Moving right on the graph is positive.
17
Find the slope of the line.
Write slope ratio.
Write slope ratio. MANDATORY STEP
Start at either point. Find the vertical rise.
Up is positive and down is negative.
y











Find the horizontal run. Going right is positive
and going left is negative.
x

Simplify.
18
Find the slope of the line.
Write slope ratio.
Start at either point. Find the vertical rise.
Up is positive and down is negative.
y













Find the horizontal run. Going right is positive
and going left is negative.
x


Simplify.
Slope is the rate of change. It will change -2
all along the line.
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Example 4A Find the slope of the line.
1. Write slope ratio.
y
2. Start at either point. Find the vertical
rise. Up is positive and down is negative.












x
3. Find the horizontal run. Going right is
positive and going left is negative.
It does not matter at which point you begin the
walk!
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Example 4B Find the slope of the line.
1. Write slope ratio.
y
2. Start at either point. Find the vertical
rise. Up is positive and down is negative.












x
3. Find the horizontal run. Going right is
positive and going left is negative.
It does not matter at which point you begin the
walk!
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Example 5 Find the slope of the line.
y
1. Write slope ratio.










2. Start at either point. Find the vertical
rise. Up is positive and down is negative.
x


3. Find the horizontal run. Going right is
positive and going left is negative.
zero ooooover the fraction line is (zeroooooo)
4. Simplify
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Example 6 Find the slope of the line.
y
1. Write slope ratio.










2. Start at either point. Find the vertical
rise. Up is positive and down is negative.

x

3. Find the horizontal run. Going right is
positive and going left is negative.
zero unnnnder the fraction line is unnnnndefined
4. Simplify
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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.
(-2,-3) and (3,-3) 3. (4,5) and (2,2)
4. (6,1) and (4,1) 5. (3,6) and
(3,1) 6. (2,2) and (1,4)
Find the slope by walking the line.
Writing the slope ratio is a mandatory step!
y
y
8.
7.












x
x


24
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.
(-2,-3) and (3,-3) 3. (4,5) and (2,2)
4. (6,1) and (4,1) 5. (3,6) and
(3,1) 6. (2,2) and (1,4)
Find the slope by walking the line.
y
y
8.
7.












x
x


25
Homework
4-A2 SKILLS PRACTICE Wkbk. Page 24 119 4 19
Plot the points and draw the line that passes
through them. Then find the slope using the
slope ratio. Skip 12.