Algebra 4-4 Study Guide: The Slope Formula (pp 254-256)
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Attendance Problems. Add or subtract.
1. 4 + (-6)
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4. 2 - (-1)
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2. -3 + 5
3. -7 - 7
Find the x and y-intercepts.
5. x + 2y = 8
6. 3x + 5y = -15
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• I can find slope by using the slope formula.
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CC.9-12.F.IF.6 Calculate and interpret the average rate of change of a function
(presented symbolically or as a table) over a specified interval. Estimate the rate of
change from a graph.*
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the amount of water in a reservoir,
is changing. (See Example 3.)
Algebra 4-4 Study Guide: The Slope Formula (pp 254-256)
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In a previous lesson, slope was described
as the constant rate of change ofSlope
a line.Song
You saw how to find the slope
of a line
(Turkey
in the Straw)
by using its graph.
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Slope
is is
rise
over
run as weyou
all know.
There
also
a formula
can use to
With
the
Y’s
on
the
top
and
the
X’s
find the slope of a line, which
is below.
usually
Subtract
the
terms
to
get
it
right.
represented by the letter m. To use this
Simplify
last
forneed
a wonderful
sight.
formula,
you
the coordinates
of
! two different points on the line.
(Chorus)
Rise over run, Y’s over X.
Rise over run, Y’s over X.
Slope Formula
Subtract the terms to get it right.
Simplify last WORDS
for a wonderful sight!
FORMULA
EXAMPLE
!
If (x , y ) and (x , y ) are If (2, -3) and (1, 4) are
slope of a line is the
! The
of the difference in
any two different points two points on a line, the
! ratio
y-values
to
the
difference
onof
a line,
thethat
slope
of
slope
line
Video Example 1. Find the slope
the line
contains
(5,
-3) of
&(the
(-1,
2). is
)
between any
the line is m = ______ .
m = _______ = ___ = -7.
! intwox-values
different points on
! the line.
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1
1
2
2
y2 - y1
x2 - x1
1
AMPLE
4 - -3
1-2
7
-1
Finding Slope by Using the Slope Formula
Find the slope of the line that contains (4, -2) and (-1, 2).
y2 - y1
m= _
x2 - x1
umbers
om right
bles are
ripts.
x sub
as
”
2 - (-2)
= _
-1 - 4
4
=_
-5
4
= -_
5
!
!
!
er 4 Linear Functions
Use the slope formula.
Substitute (4, -2) for (x 1, y 1) and (-1, 2) for (x 2 , y 2).
Simplify.
4.
The slope of the line that contains (4, -2) and (-1, 2) is - _
5
1a. Find the slope of the line that contains (-2, -2) and (7, -2).
1b. Find the slope of the line that contains (5, -7) and (6, -4).
( ) ( )
3, _
7 and _
1, _
2 .
1c. Find the slope of the line that contains _
4 5
4 5
Algebra 4-4 Study Guide: The Slope Formula (pp 254-256)
Page !3 of !9
Example 1. Find the slope of the line that contains (2, 5) and (8, 1).
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Guided Practice. Find the slope of the line that contains the following points.
7. (–2, –2) & (7, –2)
8. (5, –7) & (6, –4)
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Video Example 2. Find the slope.
A.
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B.
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⎛ 3 7⎞ ⎛ 1 2⎞
9. ! ⎜ , ⎟ & ⎜ , ⎟
⎝ 4 5⎠ ⎝ 4 5⎠
Sometimes you are not given two points to use in the formula. You might have to
choose two
a graph
or aSlope
table. Formula (pp 254-256)
Algebra
4-4points
Studyfrom
Guide:
The
Page !4 of !9
2
AMPLE
Finding Slope from Graphs and Tables
Each graph or table shows a linear relationship. Find the slope.
A
Þ
{
Let (2, 2) be (x1, y1) and (-2, -1) be (x 2 , y 2).
Ó
­Ó]ÊÓ®
­Ó]Ê£®
ä
{
Ó
Ý
{
Ó
{
y2 - y1
m= _
x2 - x1
-2
_
= -1
-2 - 2
-3
=_
-4
3
=_
4
B
Use the slope formula.
Substitute (2, 2) for (x 1, y 1) and (-2, -1) for (x 2 , y 2).
Simplify.
x
2
2
2
2
y
0
1
3
5
Step 1 Choose any two points from the table. Let (2, 0) be (x 1, y 1) and
(2, 3) be (x 2 , y 2).
Step 2 Use the slope formula.
y2 - y1
Use the slope formula.
m= _
x2 - x1
-0
_
=3
Substitute (2, 0) for (x1, y1) and (2, 3) for (x 2 , y 2).
2-2
3
Simplify.
=_
0
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The slope is undefined.
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Each graph or table shows a linear relationship. Find the slope.
2a. 8 y
2b.
Þ
­Ó]Ê{®
(8, 6)
6
Ó
Ý
4
(4, 4)
{
x
0
{
2
4
6
8
Ó
ä
Ó
­ä]ÊÓ®
Ó
{ÊÊ
{
Algebra 4-4 Study Guide: The Slope Formula (pp 254-256)
Example 2. Find the slope.
A.
B.
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Guided Practice. Each graph or table shows a linear relationship. Find the
slope.
10.
11
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12.
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13.
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Algebra 4-4 Study Guide: The Slope Formula (pp 254-256)
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Video Example 3. The graph shows the value
of a computer after x months. Find the slope of
the line and explain what the slope represents.
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Environmental Science Application
The graph shows how much water is in
a reservoir at different times. Find the
slope of the line. Then tell what the
slope represents.
Step 1 Use the slope formula.
y2 - y1
m= _
x2 - x1
- 3000
__
= 2000
60 - 20
-1000 = -25
=_
40
Water in Reservoir
Water (thousand ft3)
3
XAMPLE
(20, 3000)
3000
2500
2000
1500
1000
500
0
(60, 2000)
10 20 30 40 50 60
Time (h)
Step 2 Tell what the slope represents.
In this situation, y represents volume of water and x represents time.
change in volume
of cubic feet
_________________
So slope represents _____________ in units of thousands
.
hours
change in time
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3. The graph shows the height of a plant over a period of days.
Find the slope of the line. Then
Plant Growth
tell what the slope represents.
Height (cm)
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A slope of -25 means the amount of water in the reservoir is decreasing
(negative change) at a rate of 25 thousand cubic feet each hour.
24
20
16
12
8
4
0
(50, 20)
(30, 10)
10 20 30 40 50
Algebra 4-4 Study Guide: The Slope Formula (pp 254-256)
Page !7 of !9
Example 3. The graph shows the average electricity costs (in dollars) for operating
a refrigerator for several months. Find the slope of the line. Then tell what the
slope represents.
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12. Guided Practice. The graph shows the height of a
plant over a period of days. Find the slope of the line. Then
tell what the slope represents.
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Video Example 4: Find the slope of the line described by 3x - 5y = 15.
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Time (days)
If you know the equation that describes a line, you
can find its slope by using any two ordered-pair
solutions.
is oftenGuide:
easiestThe
to use
the ordered
pairs
contain the intercepts.
Algebra
4-4ItStudy
Slope
Formula
(ppthat
254-256)
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4
AMPLE
Finding Slope from an Equation
Find the slope of the line described by 6x - 5y = 30.
Step 1 Find the x-intercept.
6x - 5y = 30
6x - 5(0) = 30
6x = 30
6x = _
30
_
6
6
x=5
Step 2 Find the y-intercept.
6x - 5y = 30
Let y = 0.
6(0) - 5y = 30
Let x = 0.
-5y = 30
-5y
30
_
=_
-5
-5
y = -6
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Step 3 The line contains (5, 0) and (0, - 6). Use the slope formula.
y2 - y1
6-0
-6
6
_
_
_
m= _
x 2 - x 1 = 0 - 5 = -5 = 5
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4. Find the slope of the line described by 2x + 3y = 12.
Example 4: Find the slope of the line described by 4x – 2y = 16.
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r 4 Linear Functions
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ndd 256
Algebra 4-4 Study Guide: The Slope Formula (pp 254-256)
13. Guided Practice. Find the slope of the line described by 2x + 3y = 12.
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4-4 Assignment (pp 258-259) 11, 13-17, 19, 20, 21-25.
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