Algebra Lab - "Slope and Intercept"

GSP is a nice tool for finding out information about lines that Algebra Xpresser may not give. We can plot points, create the line that goes through those points, and then measure the slope of the line. Algebra Xpresser is nice because we can enter equations in point-slope form, standard form, or slope-intercept form and see a graph of our line. We are going to find out information about lines using both programs. When you see *STOP* you will have to perform some type of operation in the space provided.

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. Next, you will be looking at the x and y intercepts. Finally, you will find the slope of the line by counting rise over run. The menus you will go to will be listed in boldface print.

a) 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 with your mouse.

*STOP* Calculate the slope of the line that goes through those two points using:

m = (y2 - y1)/(x2 - x1)

b) 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.

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

d) You are now going to find the slope of the line by counting from one point to the other. Remember slope = rise/run. What is the slope of your line? __________

e) Now we will check to see if you had the correct slope. Highlight your line and then
MEASURE - SLOPE. Were you right? ______

f) Now, we are going to find the x and y intercepts. Can you tell where the line crosses the x and y axis? What is the x - intercept? _________ What is the y - intercept? ________

g) We are going to let the computer verify our answers. We want to use the trace function of the computer. You are going to have to construct a point on the line and measure its coordinates. Make sure your line is highlighted.
CONSTRUCT - POINT ON OBJECT

You should see a highlighted point on your line. We want to find out its location.
MEASURE - COORDINATES

Make sure you have the arrow tool selected. Now take the arrow and click on that new point you constructed. Drag the point up and down the line to find out the coordinates of ordered pairs that are on the line. Look in particular at x and y intercept to see if your previous conclusion was correct. Were you? _______

h) *STOP* Write the equation of the line in slope-intercept form using the slope and the y - intercept from work above.

i) GSP will allow us to measure the equation of the line to see if your work above is correct. Click off of the line so that nothing is highlighted. Now, highlight the line.
MEASURE - EQUATION.

What does the calculator show as the equation of the line? __________________

PROJECT TWO: See if you can recreate the steps above to find the slope, x - intercept, y - intercept, and equation of the line that goes through the following points.

a) (6, -4) and (1, 6) slope = ______ x-int. ______ y-int. ______

equation of the line in slope-intercept form____________________

b) (-4, 4) and (2, 8) slope = ______ x-int. ______ y-int. ______

equation of the line in slope-intercept form____________________

FILE - QUIT

Now we are going to use Algebra Xpresser to graph some linear equations. You will try to determine the slope, x-intercept, and y-intercept beforehand and then graph to verify your results.

GETTING STARTED WITH ALGEBRA XPRESSER:

Go to the APPLE and select ALGEBRA XPRESSER.

You should see a white screen with a tool bar to the right. You will see that is selected, or in other words highlighted. This is where we will type in the equations we want to graph. Make sure your CAPS LOCK is off.

We want to see a graph of the equation y = 3x + 5.

a) *STOP* Find the slope and y-intercept of the equation above. List them below.

slope = __________

y-intercept = __________

b) Graph the equation y = 3x + 5 to see if you were right. You will have to zoom in to count rise over run. Do this by creating a box around the area the part of the line that crosses the x and y axis. Find:

slope = = __________

y-intercept = __________

c) Now you are going to graph the equation, 3x - 2y = 12.

*STOP* What form is the equation in?_______________

d) Find the x-intercept, y-intercept, and slope by looking at your graph. Remember, you may have to zoom in to count the rise over run.

slope = __________

y-intercept = __________

x-intercept = __________

e) *STOP* Now you are going to determine below the y-intercept and the slope by solving your equation, 3x - 2y = 12. for y. Remember when you have your equation in the form
y = mx + b you can see the slope and y - intercept.

f) See if you can predict what the slope and y-intercept will be for the equation,
y = -2x -4.

slope = __________

y-intercept = __________

g) Graph the equation. Were you right? ______ What is the x-intercept? _____________

*STOP* How do you find the x-intercept algebraically? Show your work below

h) Calculate the slope, x-intercept, and y-intercept for the following equation:
3x - y = 3.

slope = __________

y-intercept = __________

x-intercept = __________

i) Graph the equation, 3x - y = 3 to see if you were correct. Were you?________

j) What form is the equation y - 5 = 4(x+2) in? ____________Graph it.

k) What is the slope of the line? _______ What is the y-intecept?________

l) *STOP* Solve the equation, y - 5 = 4(x+2) for y below. Can you see the slope and
y-intercept? _________