Graph . Equations of Lines. Objectives:. To find the slope of a line given 2 points. To classify a line based on its slope. To find the slope of parallel and perpendicular lines. To graph the equation of a line using slope-intercept and standard form of a line. ID: 732308
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Presentations text content in Find Slope & Rate of Change
Slide1
Find Slope & Rate of ChangeGraph Equations of Lines
Objectives:
To find the slope of a line given 2 points
To classify a line based on its slope
To find the slope of parallel and perpendicular lines
To graph the equation of a line using slope-intercept and standard form of a line
Slide2
Vocabulary
Slope
Rate
of Change
Parallel
Perpendicular
Parent
Function
Intercepts
Slope-Intercept
Form
Standard Form
Slide3
Objective 1
You will be able to find the slope between two points
Slide4
Slope
Anything that isn’t completely vertical has a slope. This is a value used to describe its incline or decline.
Slide5
Rate of Change
Slope can be used to represent an average
rate of change
.
A rate of change is how much one quantity changes (on average) relative to another.
For slope, we measure how changes relative to .
Slide6
Exercise 1Describe some real-world rates of change.
Slide7
Practical Slope
The slope or pitch of a roof is quite a useful measurement. How do you think a contractor would measure the slope or pitch of a roof?
Slide8
Pitch of a Roof
The slope or pitch of a roof is defined as the number of vertical inches of rise for every 12 inches of horizontal run.
Slide9
Slope Definition
The
slope
m
of a nonvertical line is the ratio of vertical change (the ryse) to the horizontal change (the run).ryseryse
Slide10
Exercise 2
Regulations state that a handicap ramp must not exceed one inch of rise for every linear foot of run. If the maximum rise of a handicap ramp is 2.5 feet, what is the longest horizontal length of any handicap ramp?
Slide11
Exercise 3Find the slope of the line passing through the points (
−
4,
−
5) and (6,
−2).
Slide12
Exercise 4Find the value of
k
such that the line passing through the points (
−
4, 2
k) and (k, −5) has slope −1.
Slide13
Objective 2
You will be able use slope to be
able to tell what kind of
line you have
Slide14
The Slope Game
The slope of a line indicates whether it rises or falls (L to R) or is horizontal or vertical.
m
> 0
m
< 0
m
= 0
m
=
undef
Insert
Picture
Insert
Picture
Insert
Picture
Insert
Picture
As the absolute value of the slope of a line increases, --?--.
the line gets steeper.
Slide15
Exercise 5Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.
(1, 6); (8,
−
1)
(
−4, −3); (7, 1)(−5, 3); (−5, 1)(9, 2); (−9, 2)
Slide16
Objective 3
You will be able to find the slopes of parallel and perpendicular lines
Slide17
Parallel and Perpendicular
Two lines are
parallel lines
iff
they are coplanar and never intersect.
Two lines are perpendicular lines iff they intersect to form a right angle.
Slide18
Parallel and Perpendicular
Two lines are
parallel lines
iff
they have the same slope.
Two lines are perpendicular lines iff their slopes are negative reciprocals.
Slide19
Exercise 6 Tell whether the pair of lines are parallel, perpendicular, or neither
Line 1: through (-2, 1) and (0, -5)
Line 2: through (0, 1) and (-3, 10)
Line 1: through (-2, 2) and (0, -1)
Line 2: through (-4, -1) and (2, 3)
Slide20
Exercise 7
If two distinct lines are parallel, what do you know about their
y
-intercepts?
If one of two perpendicular lines has a slope of 1/
a and a < 0, is the slope of the other line positive or negative?
Slide21
Objective 4
You will be able to graph the equation of a line in slope- intercept or standard form
Slide22
Parent FunctionsWho is the simplest member of your family? Well, in math, the simplest member of a
family of functions
is called the
parent function
.
Family of Linear FunctionsLinear Parent Function
Family of Linear Functions
Linear Parent
Function
Slide23
Parent FunctionsWho is the simplest member of your family? Well, in math, the simplest member of a
family of functions
is called the
parent function
.
Family of Quadratic FunctionsQuadratic Parent Function
Family of
Quadratic
Functions
Quadratic
Parent
Function
Slide24
Parent FunctionsWho is the simplest member of your family? Well, in math, the simplest member of a
family of functions
is called the
parent function
.
Family of FunctionsParent FunctionA group of functions that share common characteristicsSimplest member of the family
Slide25
Parent Functions
Linear parent function:
or
All other linear functions can be formed with transformations on the parent function.
Slide26
Intercepts
Click me!
The
-intercept
of a graph is where it intersects the
-axis.
The
-intercept
of a graph is where it intersects the
-axis.
Slide27
Slope-Intercept
Slope-Intercept Form of a Line:
If the graph of a line has slope
and a
-intercept of (0,
), then the equation of the line can be written in the form
Slope
-intercept
Slide28
4.
3.
2.
1.
Slope-Intercept
To graph an equation in slope-intercept form:Draw line
Solve for
Use
to plot more points
Plot
Slide29
Exercise 8aWithout your graphing calculator, graph each of the following:
Slide30
Exercise 8bWithout your graphing calculator, graph each of the following:
Slide31
Standard Form
Standard Form of a Line
The standard form of a linear equation is
, where
and
are not both zero.
Generally taken to be integers
Slide32
Standard FormTo graph an equation in standard form:
Write equation in standard form.
Let
x
= 0 and solve for
y. This is your y-intercept.Let y = 0 and solve for x. This is your x-intercept.Connect the dots.
Slide33
3.
2.
1.
Standard Form
To graph an equation in standard form:
Let
Let
Draw line
Solve for
Solve for
This is the
-intercept
This is the
-intercept
Slide34
Exercise 9aWithout your graphing calculator, graph each of the following:
Slide35
Exercise 9bWithout your graphing calculator, graph each of the following:
Slide36
Exercise 10For an equation in standard form,
A
x
+
B
y = C, what is the slope of the line in terms of A and B?
Slide37
Horizontal and Vertical Lines
Horizontal
Line
The
graph of
is a horizontal line through . Vertical LineThe graph of
is a
vertical
line
through
.
Slide38
Exercise 11Graph each of the following
:
Slide39
Find Slope & Rate of ChangeGraph Equations of Lines
Objectives:
To find the slope of a line given 2 points
To classify a line based on its slope
To find the slope of parallel and perpendicular lines
To graph the equation of a line using slope-intercept and standard form of a line
Download this presentation
DownloadNote - The PPT/PDF document "Find Slope & Rate of Change" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Presentations text content in Find Slope & Rate of Change
Find Slope & Rate of ChangeGraph Equations of Lines
Objectives:
To find the slope of a line given 2 points
To classify a line based on its slope
To find the slope of parallel and perpendicular lines
To graph the equation of a line using slope-intercept and standard form of a line
Slide2Vocabulary
Slope
Rate
of Change
Parallel
Perpendicular
Parent
Function
Intercepts
Slope-Intercept
Form
Standard Form
Slide3Objective 1
You will be able to find the slope between two points
Slide4Slope
Anything that isn’t completely vertical has a slope. This is a value used to describe its incline or decline.
Slide5Rate of Change
Slope can be used to represent an average
rate of change
.
A rate of change is how much one quantity changes (on average) relative to another.
For slope, we measure how changes relative to .
Slide6Exercise 1Describe some real-world rates of change.
Slide7Practical Slope
The slope or pitch of a roof is quite a useful measurement. How do you think a contractor would measure the slope or pitch of a roof?
Slide8Pitch of a Roof
The slope or pitch of a roof is defined as the number of vertical inches of rise for every 12 inches of horizontal run.
Slide9Slope Definition
The
slope
m
of a nonvertical line is the ratio of vertical change (the ryse) to the horizontal change (the run).ryseryse
Slide10Exercise 2
Regulations state that a handicap ramp must not exceed one inch of rise for every linear foot of run. If the maximum rise of a handicap ramp is 2.5 feet, what is the longest horizontal length of any handicap ramp?
Slide11Exercise 3Find the slope of the line passing through the points (
−
4,
−
5) and (6,
−2).
Slide12Exercise 4Find the value of
k
such that the line passing through the points (
−
4, 2
k) and (k, −5) has slope −1.
Slide13Objective 2
You will be able use slope to be
able to tell what kind of
line you have
Slide14The Slope Game
The slope of a line indicates whether it rises or falls (L to R) or is horizontal or vertical.
m
> 0
m
< 0
m
= 0
m
=
undef
Insert
Picture
Insert
Picture
Insert
Picture
Insert
Picture
As the absolute value of the slope of a line increases, --?--.
the line gets steeper.
Slide15Exercise 5Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.
(1, 6); (8,
−
1)
(
−4, −3); (7, 1)(−5, 3); (−5, 1)(9, 2); (−9, 2)
Slide16Objective 3
You will be able to find the slopes of parallel and perpendicular lines
Slide17Parallel and Perpendicular
Two lines are
parallel lines
iff
they are coplanar and never intersect.
Two lines are perpendicular lines iff they intersect to form a right angle.
Slide18Parallel and Perpendicular
Two lines are
parallel lines
iff
they have the same slope.
Two lines are perpendicular lines iff their slopes are negative reciprocals.
Slide19Exercise 6 Tell whether the pair of lines are parallel, perpendicular, or neither
Line 1: through (-2, 1) and (0, -5)
Line 2: through (0, 1) and (-3, 10)
Line 1: through (-2, 2) and (0, -1)
Line 2: through (-4, -1) and (2, 3)
Slide20Exercise 7
If two distinct lines are parallel, what do you know about their
y
-intercepts?
If one of two perpendicular lines has a slope of 1/
a and a < 0, is the slope of the other line positive or negative?
Slide21Objective 4
You will be able to graph the equation of a line in slope- intercept or standard form
Slide22Parent FunctionsWho is the simplest member of your family? Well, in math, the simplest member of a
family of functions
is called the
parent function
.
Family of Linear FunctionsLinear Parent Function
Family of Linear Functions
Linear Parent
Function
Slide23Parent FunctionsWho is the simplest member of your family? Well, in math, the simplest member of a
family of functions
is called the
parent function
.
Family of Quadratic FunctionsQuadratic Parent Function
Family of
Quadratic
Functions
Quadratic
Parent
Function
Slide24Parent FunctionsWho is the simplest member of your family? Well, in math, the simplest member of a
family of functions
is called the
parent function
.
Family of FunctionsParent FunctionA group of functions that share common characteristicsSimplest member of the family
Slide25Parent Functions
Linear parent function:
or
All other linear functions can be formed with transformations on the parent function.
Slide26Intercepts
Click me!
The
-intercept
of a graph is where it intersects the
-axis.
The
-intercept
of a graph is where it intersects the
-axis.
Slide27Slope-Intercept
Slope-Intercept Form of a Line:
If the graph of a line has slope
and a
-intercept of (0,
), then the equation of the line can be written in the form
Slope
-intercept
Slide284.
3.
2.
1.
Slope-Intercept
To graph an equation in slope-intercept form:Draw line
Solve for
Use
to plot more points
Plot
Slide29Exercise 8aWithout your graphing calculator, graph each of the following:
Slide30Exercise 8bWithout your graphing calculator, graph each of the following:
Slide31Standard Form
Standard Form of a Line
The standard form of a linear equation is
, where
and
are not both zero.
Generally taken to be integers
Slide32Standard FormTo graph an equation in standard form:
Write equation in standard form.
Let
x
= 0 and solve for
y. This is your y-intercept.Let y = 0 and solve for x. This is your x-intercept.Connect the dots.
Slide333.
2.
1.
Standard Form
To graph an equation in standard form:
Let
Let
Draw line
Solve for
Solve for
This is the
-intercept
This is the
-intercept
Slide34Exercise 9aWithout your graphing calculator, graph each of the following:
Slide35Exercise 9bWithout your graphing calculator, graph each of the following:
Slide36Exercise 10For an equation in standard form,
A
x
+
B
y = C, what is the slope of the line in terms of A and B?
Slide37Horizontal and Vertical Lines
Horizontal
Line
The
graph of
is a horizontal line through . Vertical LineThe graph of
is a
vertical
line
through
.
Slide38Exercise 11Graph each of the following
:
Slide39Find Slope & Rate of ChangeGraph Equations of Lines
Objectives:
To find the slope of a line given 2 points
To classify a line based on its slope
To find the slope of parallel and perpendicular lines
To graph the equation of a line using slope-intercept and standard form of a line
Slide40Slide41