Learn how to visualize equivalent transformations of equations with GeoGebra

Step 1: Try out the GeoGebra applet

Change the value of the slider in order to explore how the lines change.

Step 2: Watch the tutorial video

Step 3: Create the construction yourself

Construction Steps

1.

In the CAS View, enter the equation x - 2 = 1 and hit the Enter key.

2.

In order to visualize the left side term of the equation, enter LeftSide[#1]. Then, click on the Show/Hide symbol to the left of line 2 in order to show the graph in the Graphics View.

Hint: The input #1 refers to the output of the row 1, so you don’t have to enter the equation again.

3.

Also visualize the right side term of the equation by entering RightSide[#1]and showing the graph. Does not work now!

4.

In the Graphics View, create a slider a using the slider tool. In the appearing window set the slider name to a = 0 and change the Increment: 1. Then, click Apply.

5.

In the CAS View, enter (#1) + a.

Hint: This will allow you to transform the equation using slider a.

6.

Enter f_a(x):=f + a and hit the Enter key. Then, show the graph of this new term.

7.

Enter g_a(x):=g + a and show the graph of the resulting term.

8.

In the Graphics View, use the Move tool in order to simplify the equation by changing the value of the slider.

Task

How can this example help you understand why equivalent transformations can be applied to an equation?
Hint: You might want to show the graph of the equation in row 1 in the Graphics View while exploring how changing the value of slider a affects the left and right side of the equation and the solution.