Department of Mathematics
Exploring Straight Line Graphs
The straight line graph y = mx + c
Explore the effects of varying m and c
Once you have turned the calculator on press the
menu button, this will take you to the following
screen.
Use the cursor key to highlight option 5:Graph
and press the EXE button. Your screen should now
look like this
Using the X,θ,T button, enter the equation y = x
Press F6 to drawn the graph, followed by F3
Set the scale as shown in the picture.
Press EXIT to return to your graph
Department of Mathematics
By looking at your graph screen, describe the graph y = x.
Changing the value of C
Press F6 to take you back to the Y= screen
Enter y = x + 1 into Y2=
View your graph by pressing F6
Describe the graph of y = x +1 compared to the graph of y = x
Now plot the graph y = x - 1 and view
Describe the graph of y = x −1 compared to the graph of y = x
What effect does changing the number c have on the graph of the function y = mx + c?
Changing the number m
Delete Y2 and Y3, by highlighting each equation
using the arrow keys and pressing F2 followed by F1
Your screen should look like this
View the graph by pressing F6
Describe the graph of y = x
Plot y = 2x
Now view your graph
Now plot and view y = 3x
Describe the graph of y = 3x compared to y = x
What effect does increasing the value of m have on the graph of the function y = mx
Plot and view the graph of y = -x
Describe the graph of y = -x compared to the graph of y = x
Plot y = -2x on the same graph
Describe the graph of y = -2x compared to the graph of y = -x
What effect does the negative value of m have on the graph of the function y = mx + c?
Exploring y = mx + c
Exercise 1
Recreate the following graphs
Exercise 2
The kite in the figure has been formed from four straight-line graphs. Recreate the drawing using
the given information
Exercise 3: Simultaneous Equations
Solve the following pairs of simultaneous equations using straight -line graphs.
(a)
y=x−1
y = 3x − 5
(b)
y = 2x + 1
y = 3x − 2
(c)
2y = 5x + 1
3y = 7x − 8
Extension: Investigation of Quadratics
Draw graphs of the following formulas
y = x2
y = −x2
y = (x − 4)2
y = x2 − 4
y = 4 − x2
Describe the properties of your graphs
These are called quadratic graphs. Choose other formulas which will give you quadratic graphs.
How could you describe your graphs in terms of transformations of the two graphs y = x2 and y =
−x2?