Graphing Slope-Intercept Form

Graphing Slope-Intercept Form

Stand-Alone Instructional Resource

CEP811

Deborah Johnson

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Students will master the following 8th grade Introduction to Algebra and Geometry Instructional Standards:

Lesson Objectives

Graph linear equations in slope intercept form y = mx + b (GPS) (8MA_E2009-58)

Determine the meaning of the slope and y-intercept in a given situation (GPS) (8MA_E2009-57)

Time to Learn!

Interpret slope as a rate of change (GPS) (8MA_E2009-56)

Definition ofSlope-Intercept

Form

What do you need to know about slope-intercept form?First!

Click on the boxes below to explore each definition!

Second!

Let’s Graph!

Definition of Slope

“The constant change of a line is called the slope of the line.” – Holt Textbook Pg 311

You should know two things about slope:

The “Types” of Slope

How to “Count”

Slope

If you are not familiar with either topic, click on the box for a quick review.

DefinitionsHome Page!

We “read” slope just like we would read a book: From LEFT to RIGHT.

The direction your line moves indicates the type of slope.

Types of SlopeThere are Four

Click on the green boxes to further explore each type! Slope Home Page!

It does not matter WHERE the line is located on the coordinate plane, but rather the direction. Often, we think of positive slope as a line going UP.

We can see slope in real life!Can you see the POSITIVE slope in the

picture above?

(click on the picture to check your answer)

With POSITIVE slope, the line rises from left to right.

With NEGATIVE slope, the line falls from left to right.

Often, we think of negative slope as a line going DOWN.

Check out the picture to the left! Can you find the NEGATIVE slope?

(click on the picture to check your answer)

Zero slope always looks like a HORIZONTAL line.

An easy way to remember this is by visualizing a person walking on your line.The person has ZERO slope because they do not go up or down.

Click on the graph to see this!

VERTICAL lines have undefined slope.

Think of “undefined” slope as having no where else to go, but up…or down!

Where would our person go in this graph? (click on the graph to see!)

Let’s Practice!Tell whether the slope of each line is positive, negative, zero, or undefined.Click on the graph to check your answer!

PositiveThe graph rises from left to right.

NegativeThe graph falls from left to right.

NegativeThe graph falls from left to right.

UndefinedThe graph is a vertical line.

ZeroThe graph is a horizontal line.

PositiveThe graph rises from left to right.

Slope!

We graph slope using…

runrise change in y

change in x

Slope Home Page!

Ready to Explore?Click the Video Link on the Next Slide!

“Counting” Slope Video Remember

runrise

slope

You need at least two points to graph slope

“Read” slope from left to right

Click on the Video Above to ViewClick HERE to view online.

Can You Find It? Using , find the slope of the line.runrise

A. - ⅓

B. -3

C. ⅓

D. 3

1.

Should you have a positive or negative slope?

Should you have a positive or negative slope?

Remember, rise ↕ over run ↔.

Correct!

Great Job!!!

Click on your answer choice.

Can You Find It? Using , find the slope of the line.runrise

2.

A. 2

B. -2

C. ½

D. - ½

Should you have a positive or negative slope?

Should you have a positive or negative slope?

Remember, rise ↕ over run ↔.Correct!

Great Job!!!

Click on your answer choice.

Need more practice?

Ready to move on?

Using algebra.help, look at each graph and enter the appropriate slope. Click on “Check Worksheet” at the

bottom of the page to check your work!

Practice Here!

Back to Definitions!

“The y-intercept is the y-coordinate of the point where the graph intersects the y-axis. The x-coordinate of this point is always 0.”

– Holt Textbook Pg 303

“The x-intercept is the x-coordinate of the point where the graph intersects the x-axis. The y-coordinate of this point is always 0.”

– Holt Textbook Pg 303

Let’s See How to Remember This

Vocabulary!

(0, y-intercept)

(x-intercept, 0)

DefinitionsHome Page!

http://espn.go.com/video/clip?id=5667192

Football!When you hear “intercepts,” think:

Think of your line like the “path” Denard Robinson wanted his football to be thrown.

The y-intercept represents the point

where the line crosses the y-axis.

For our story, this is where Chris L. Rucker “intercepts” the ball.

The x-intercept represents the point where the line

crosses the x-axis.

For our story, let’s suppose Michigan State“intercepts” the ball again

at the x-axis.

Click on the Player to Hear a Story about

the Video!

Let’s Practice! Find the x- and y- intercepts.

Where does the line cross the y-axis? Where does the line cross the y-axis?

Where does the line cross the x-axis? Where does the line cross the x-axis?

The x-intercept is:

The y-intercept is:

The x-intercept is:

The y-intercept is:

5

-4

2

1

A. B.

Your Turn! Find the x- and y- intercepts.

The x-intercept is:

The y-intercept is:

The x-intercept is:

The y-intercept is:

C. D.

4

Click on the question to view the answer.

-1

2 4

Slope-Intercept Form

y = mx + b

“If a line has slope m and the y-intercept b, then the line is described by the equation y = mx + b.”

– Holt Textbook Pg 335

slope y-intercept

DefinitionsHome Page!

Slope-Intercept Form

Can you recognize slope-intercept form?

Let’s Play…

Slope-Intercept Form

Not!or

2x4y

orSlope-Intercept Form

Not!

Skip to NextProblem!

Slope-InterceptDefinition!

Click on your answer!

Correct!2x4y

What is the y-intercept?

What is the slope?4-2

Click on the question to view the answer. NextProblem!

Try Again!

y = mx + b

slope y-intercept

Remember…

GoBack!

6x2y

orSlope-Intercept Form

Not!

Skip to NextProblem!

Slope-InterceptDefinition!

GoBack!

Click on your answer!

Try Again!y = mx + bNotice! “y” should be

ISOLATED (by itself) on one side of the equation

Remember…

GoBack!

Correct!6x2y

Is NOT in slope-intercept form!Check out how to

re-write this equation in slope-

intercept form!

6x2y + 2x+ 2x

y = 2x + 6The slope is 2.

The y-intercept is 6.Next

Problem!

x43

y

orSlope-Intercept Form

Not!

Slope-InterceptDefinition!

GoBack!

Click on your answer!

Correct!

What is the y-intercept?

What is the slope?-3/40

Click on the question to view the answer.

x43

y + 0

DefinitionsHome Page!

Time to Learn GRAPHING!

Try Again!y = mx + b

slope y-intercept

Remember…

GoBack!

Hint: If there is NO y-intercept, would we have to write zero?

Graphing Slope-Intercept Form

First!

Second!

Graphing Slope-

Intercept Form

Matching Equationsto Graphs

Back toDefinitions

Home Page!

y = mx + b

slope y-intercept

Remember…Slope-intercept form is:

Click on the Video Above to View

Graphing Slope-Intercept Form

runrise

slope

FIRST, always plot the y-intercept.

SECOND, graph your slope.

Click HERE to view online.

Let’s Practice!

Graphing Slope-Intercept Form

Using the following math applet, practice graphing

slope-intercept form.

Remember! FIRST plot the y-intercept,

THEN plot the slope.

Matching

Equations

to Graphs

Example 1

y = mx + b m = slope

b = y-intercept

FIRST find the y-intercept:b =

y = __ x + ___

- 4

NOW count the slope :runrise

click here to continue

m =2

y = 2x - 4

21

On the graph, click on the correct y-intercept.

?- 4

2watch the graph

which means

Matching

Equations

to Graphs

Example 2

y = mx + b m = slope

b = y-intercept

FIRST find the y-intercept:b =

y = __ x + ___

3

NOW count the slope :runrise

click here to continue

m = -½

y = -½x+3

-12

On the graph, click on the correct y-intercept.

?3

-½watch the graph

which means

Let’s Practice!Identify the equation of the line written in slope-intercept

form that matches the provided graph.

2x32

y

3x32

y

2x23

y

2x32

y A.

B.

C.

D.

Try Again!Check Your Slope!

Should your slope be Positive or Negative?

Did you mix up ?runrise

GoBack!

Try Again!Check Your Intercept!

y = mx + b

Make sure you picked the “Y” intercept and not the “X” intercept!

GoBack!

Correct!

2x32

y Next

Problem!

Let’s Practice!Identify the equation of the line written in slope-intercept

form that matches the provided graph.

A.

B.

C.

D.

2x31

y

3x2y

2x3y

1x3y

Try Again!Check Your Slope!

Should your slope be Positive or Negative?

Did you mix up ?runrise

GoBack!

Try Again!

GoBack!

Check Your Intercept!

y = mx + b

y-intercept

Correct!

2x3y Next

Problem!

Final Challenge!Write the equation of the line for each provided graph. To check you answer, click on the

graph!

Need a Hint?

Click HERE to view the

equations that need to be

matched to the graphs!

3xy

2xy

4x34

y

2x23

y

5x25

y

4x34

y

5x25

y

2x23

y 3xy

2xy

You Did It!You have successfully completed the

“Graphing Slope-Intercept Form Stand-Alone Instructional Resource!”

Great

Job!!!

Resources

Author: Deborah Johnson Created in: Microsoft PowerPoint

Clip art: Microsoft PowerPoint

Definitions and math images: Holt Algebra 1 TextbookHolt, Rinehart and Winston Publications

http://www.algebrahelp.com/worksheets/view/graphing/slope.quizhttp://espn.go.com/video/clip?id=5667192http://www.ltcconline.net/greenl/java/BasicAlgebra/LineGraph/LineGraph.htm

Websites:

Videos: Created by Deborah Johnson using Interwrite Learning

Sound: Microsoft PowerPoint & Soungle