Find Slope & Rate of Change PowerPoint Presentation, PPT - DocSlides

Find  Slope & Rate of Change PowerPoint Presentation, PPT - DocSlides

2018-11-21 6K 6 0 0

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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

Slide40

Slide41


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