Algebra

1. Algebra Linear Equations y=mx+b Using Geogebra to Understand Slope and Intercepts

2. Follow these lesson directions as you learn about Linear Equations

3. 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

4. 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,.

5. Open View. Click on Grid

6. Click Move Graphics View and center the origin using your cursor Origin (0, 0)

7. Think!!! At a minimum, how many points define a straight line?________

8. 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

9. 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

10. Open Cursor button. Move Point B to (2, 4) and Point A to (-4, -2)

11. Open Point Button. Click on Intersect Two Objects. Directions Mark the y-intercept Mark the x-intercept

12. 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.

13. 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.

14. 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.

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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.

21. 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.

22. 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.

23. 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.

24. 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.

25. 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.

26. 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.

27. 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