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Algebra. Linear Equations y= mx+b Using Geogebra to Understand Slope and Intercepts. Follow these lesson directions as you learn about Linear Equations. Go to my website: www.denisekapler.org Click on Resources, then Math Class Resources Under Tools, click on Geogebra

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algebra

Algebra

Linear Equations

y=mx+b

Using Geogebra to

Understand Slope and Intercepts

slide3

Go to my website: www.denisekapler.org

Click on Resources, then Math Class Resources

Under Tools, click on Geogebra

From Geogebra site, click on Applet Start

Give the applet time to load

slide4

You should be here

If not, try the following :

Check that you followed the steps correctly on the preceding page

Ask your partner for assistance

If you still need assistance , ask your teacher,.

slide7

Think!!!

At a minimum, how many points define a straight line?________

slide8

Open Line Button. Click on Snap two points onto the grid: Point A and Point B

You may use the undo button under edit, if needed

At a minimum, two points define a straight line

slide9

Open Cursor Button. Click on Move and practice moving the line about the grid

Directions

Click on Point A or Point B

Move them around

slide11

Open Point Button. Click on Intersect Two Objects.

Directions

Mark the y-intercept

Mark the x-intercept

slide12

Calculate the slope of the line. Open the button indicated, and click on Slope

Direction to find slope

Click on Point A

Note that slope is shown on graph

Note that slope is now listed on the far left.

slide13

Calculate the slope of the line. Open the button indicated, and click on Slope

Direction to find slope

Click on Point A

Note that slope is shown on graph

Note that slope is now listed on the far left.

slide14

Document your work on paper. Exhibit A Linear Equation defined by x and y intercepts

Screen Print Your Graph and Print it on Paper

On your graph, label the following:

a. Point A and Point B – the original two points that defined the graph

b. The y-intercept

c. Also, write down the point representing the y-intercept in coordinate form.

d. The x-intercept

e. Also, write down the point representing the x-intercept in coordinate form.

slide15

Open the Line Relationship Button. Click on Parallel Line.

You will use this tool to draw a line through Point A that is parallel to the x-axis.

Direction to create a parallel line

Click on Point A

Click on the x-axis

slide16

Open the Line Relationship Button. Click on Perpendicular Line.

You will use this tool to draw a line through Point B that is perpendicular to the x-axis.

Directions

To create a perpendicular line to the x-axis

Click on Point B

Click on the x-axis

slide17

Open the Point Button. Click on Intersect Two Objects.

When two lines intersect they form a Point of Intersection

or are coinciding lines (the same line).

Directions

To create Point of Intersection

Click on the point where Line BE and Line AE intersect.

This will be Point E

slide18

Open Tools. Click on Distance or Length

Directions

To find the length of line segments

To find the length of BE. Click on Point B then click on Point E Note this measurement is the rise .

Repeat the above steps to find the length of AE. Note this measurement = run .

Use the move button to position the length measures so you can read them easily

slide19

Document your work on paper. Exhibit B Rise and Run

x and y intercepts

Point of Intersection of Line BE and AE = Point E

Directions

Screen Print

Print your work

Label the rise and run

Label the y-intercept

Label the x-intercept

Label the Point of Intersection of Line BE and Line AE. This is Point E

slide20

Document your work on paper. Exhibit C Equation of Line 1 in Slope Intercept Form

Directions

Screen Print

Print your work

Label the rise

Label the run

Calculate the slope using the rise and run. Show all your work.

Label the y-intercept

Label the x-intercept

Write down the equation of this line in Slope Intercept Form.

slide21

Document your work on paper. Exhibit D Equation of Line 2 in Slope Intercept Form

Move your Point B and Point A around on the grid.

Directions

Screen Print

Print your work

Label the rise and run

Calculate the slope

Label the y-intercept

Label the x-intercept

Write down the equation of this line in Slope Intercept Form.

slide22

Document your work on paper. Exhibit E Positive Slope

Move your Point B and Point A around on the grid to show a positive slope.

Directions

Screen Print

Print your work

Label the rise and run

Find the slope

Label the y-intercept

Label the x-intercept

Write down the equation of this line in Slope Intercept Form.

slide23

Document your work on paper. Exhibit F Negative Slope

Move your Point B and Point A around on the grid to show a negative slope.

Directions

Screen Print

Print your work

Label the rise and run

Determine the slope

Label the y-intercept

Label the x-intercept

Write down the equation of this line in Slope Intercept Form.

slide24

Document your work on paper. Exhibit G Zero Slope - no change in y

Move your Point B and Point A around on the grid to show a zero slope.

Directions

Screen Print

Print your work

Label the rise and run

Calculate the slope

Label the y-intercept

Label the x-intercept

Write down the equation of this line in Slope Intercept Form.

slide25

Document your work on paper. Exhibit H Undefined Slope – no change in x

Move your Point B and Point A around on the grid to show an undefined slope.

Directions

Screen Print

Print your work

Label the rise and run

Find the slope

Label the y-intercept

Label the x-intercept

Write down the equation of this line in Slope Intercept Form.

slide26

Document your work on paper. Exhibit I Direct Variation

  • Move your Point B and Point A around on the grid to show Direct Variation.
  • Note: Direct variation occurs when the y‐intercept = 0.

Directions

Screen Print

Print your work

Label the rise and run

Calculate the slope

Label the y-intercept

Label the x-intercept

Write down the equation of this line in Slope Intercept Form.

slide27

Check to be certain you have completed and properly labeled all Exhibits

Exhibit A Linear Equation defined by x and y intercepts

Exhibit B Rise and Run

x and y intercepts

Point of Intersection of Line BE and AE = Point E

Exhibit C Equation of Line 1 in Slope Intercept Form

Exhibit D Equation of Line 2 in Slope Intercept Form

Exhibit E Positive Slope

Exhibit F Negative Slope

Exhibit G Zero Slope - no change in y

Exhibit H Undefined Slope – no change in x

Exhibit I Direct Variation

Title Page

Your name

Algebra I , Mrs. Kapler

Date

Portfolio: Linear Equations

Learning Through Geogebra

Staple your project together.

Turn in your work when completed.

Thank you!

Mrs. Kapler