GSP Lab for Linear Equations

Instructions for beginning:

Go under APPLE to GSP.
Click on the white area of your screen to remove the logo.
Click on the double box on the top right area of your screen to have your "piece of paper" take up the entire screen.

Go under GRAPH to CREATE AXES.
Click on the point (1,0) and drag this adjuster point toward (0,0) until you can see -10 through 10 on each axis.
Go under GRAPH to SHOW GRID.

PROJECT ONE:
You are going to plot a couple of points, construct the line that goes through those points, and find out the equation of the line using the computer. You will then trace some ordered pairs of your equation that are solutions of your equation. The menus you will go to will be listed in boldface print.

GRAPH - PLOT POINTS
TYPE 3 (tab) 5 (return)
TYPE -4 (tab) -2 (return)
click on PLOT
The computer should have plotted those two points. Make sure they are highlighted. If not, hold down the shift key and click on each point.

DISPLAY - SHOW LABELS (This helps you to identify the two points.)
Go to the toolbar on the left. Click on the line segment and drag out to the line tool. DO NOT construct the line that goes through those two points by drawing it. We are going to have the computer construct the line that goes through those two points. This will ensure that the line cannot be moved.

CONSTRUCT - LINE
Make sure your line is highlighted if not select the line by clicking on it with the mouse.
DISPLAY - COLOR - RED

You are now going to find the equation of the line by letting the computer "measure" it.
Make sure your red line is highlighted.
MEASURE - EQUATION
The equation of the line we constructed is y = ________________.

You are now going to find some other ordered pairs that are on that line. These are solutions for your equation. Can you see four definite ordered pairs? What are they?

_______, _______, _______, and _________.

In order to trace we are going to construct a trace point on our line.
CONSTRUCT - POINT ON OBJECT
You should see a highlighted point on your line. We want to find out its location.
MEASURE - COORDINATES

What is the location of that point? ___________

Go to the toolbar and select the arrow tool. Move the point with the arrow and you will see that the coordinates change. This is like your "trace" key. Find four ordered pairs that are solutions for your equation and list them below:

___________, ____________, ___________, ____________


Compare and contrast the graphing program on GSP with your graphing calculators below in a paragraph.








PROJECT TWO:
You are now going to follow some of the same procedures you used in project one to:

1) Find the equation of the line that goes through the points (6, -4) and (1, 6). Create this line on the same coordinate plane you used in project one. Do not delete the red line. Make your new line blue.

The equation of the line is y = ______________.

What are some ordered pairs that are solutions of your linear equation?

___________, ___________, ____________, ____________.

2) Find the point that the red line and blue line have in common. ______________

3) Prove below that the ordered pair they have in common is a solution for both.





PROJECT THREE:

A) Get a new coordinate plane by recreating the steps from the introduction on a new sheet of paper. You are now going to pick two points that will be used to construct a horizontal line. You may want to look at your coordinate plane and visualize what they ordered pairs must look like. Follow the same steps that you used in project one and two.

The equation of the line is y = ______________.

What are some ordered pairs that are solutions of your linear equation?

___________, ___________, ____________, ____________.




B) Recreate the steps for (A) to create a vertical line.


The equation of the line is y = ______________.

What are some ordered pairs that are solutions of your linear equation?

___________, ___________, ____________, ____________.


PROJECT FOUR

Recently we talked about the inverse of a function. Plot the points, (1,1), (3,4), and (2,5). Connect these with line segments. What figure do you have? __________________


What will the inverse look like? Before you plot the inverse of the set of ordered pairs, predict what will happen below.



Write down the inverse of the set of ordered pairs - ________________________________.

Plot the points, connect with line segments and describe what happened below.





Take your original ordered pairs and multiply them all by -1. Write down the new set of ordered pairs - ___________________________________.

Plot the points, connect with line segments and describe what happened below.



Take your original ordered pairs and add 2 to each one. Write down the new set of ordered pairs - _________________________________________.

Plot the points, connect with line segments and describe what happened below.