Education Technology

Understanding the Linear Equation (Function Families)

Published on 11/14/2006

Activity Overview

I used this activity with my grade nines to assist their understanding of the parts of the equation y=mx+b.

Before the Activity

It is assumed that the students have had some practice entering equations on the calculator and graphing and tracing them.
Students need to log into NavNet solely for the purpose of Screen Capture.

(I've attached a student handout and the above with screenshots)

During the Activity

1. After students have logged into NavNet have them quit and go to the Y= screen

2. Enter the equations y=2x, y=2x+1, y=2x-1, y=2x+2

3. Graph them
Error message? deselect Plot1 in ?y=? menu;
Only plots one equation at a time? Cannot turn on more than one equal sign? Go to the Apps menu and select Transfrm and select Uninstall (or install it then Uninstall it)

4. Adjust window settings to separate lines more clearly

5. Trace (do not move left or right) ? Use screen capture to show students what their screen should look like and to help illustrate the following.

6. Note the equation in the upper right and look at the (X,Y) coordinates at the bottom of the screen

7. Move up or down once and compare the equation again to the current coordinates; notice anything? (don?t answer aloud)

8. Compare again with the other two lines; See a connection?

9. Capture screens with an example of each at once and make the comparisons one by one

10. Conclusion? It appears that the number all alone corresponds to the y-intercept!

11. What do all the lines have in common? What do the equations have in common? So does the 2 beside the x correspond to the angle of the line?

Part Two

12. Replace the four equations with these: y=x+3, y=2x+3, y=-x+3, y=-2x+3; they can type them over top of the equations already there or clear each one first

13. Adjust Window settings

14. Graph and Trace but do not move

15. What do the lines have in common? What do the equations have in common?

16. Conclusion: The number all alone corresponds to the y-intercept.

17. Move right to (1,4) then move up or down; What is different about the lines? (direction) What is different about the equations? Notice what a negative indicates? Which lines are steeper? (x=1x, -x=-1x)

18. Does any part of the equation indicate where the line crosses the x axis?

19. Extension: make a spider web

After the Activity

A good follow-up to this is Transformations on the graphing calculator.