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Graphing Calculator Graphing with the TI-83 Plus/TI-84 Plus
I. Introduction
The TI-84 Plus graphing calculator has greater memory capacity, is faster, and has a higher contrast screen than the TI-83 Plus model. Aside from these differences, the two calculators have virtually the same keyboards and they are keystroke-for-keystroke compatible. This is also true of the older TI-83 and TI-84 models. All TI-83 and 84 models have fifty keys, many of which perform multiple functions when used in combination. Each key has a symbol printed on its face. When a key is pressed the calculator does whatever is printed on the face of the key. This is often referred to as the primary function of the key. For example, the primary function of the ON key is to turn the calculator on, the + key performs addition, and x^2 raises numbers to the second power. In addition to their primary functions many keys have second, or shifted functions. These are the symbols written in yellow and green above the keys. To have the calculator do what is written in yellow you must first press the 2nd (yellow) key. To type letters into the calculator you must first press the ALPHA (green) key.
II. Plotting Points in a Scattergram x
y 25 28 58 130
We can use the calculator to create a scattergram of the data displayed in the table at right. As you follow the steps below, compare the screen on your calculator to the screenshots to the right.
Press the STAT key. Your calculator window should look like the picture at the right.
Press 1 (Edit). If you have any numbers (data) in the lists ( L 1 , L 2 , or L 3 , etc.) you can clear them by pressing the up arrow to move the cursor to the top of the column, then press the CLEAR key, followed by ENTER. Use or to get to the next list, and repeat the steps to clear all the lists. NOTE: if you press DEL instead of CLEAR , the entire column will vanish. If you do this by accident, pres STAT 5 (SetUpEditor) then ENTER to replace the deleted column.
To enter the new data, press the STAT key, then 1 (Edit). Enter the X- values from the table in L 1 by typing 2 ENTER , 5 ENTER , 8 ENTER , 11 ENTER. Move the cursor to L 2 and enter the Y-values; 25, 28, 58, and 130 in the same way.
Now press the Y= key. If you have any equations on this screen, press CLEAR. Use the and keys to move from Y1= to Y2= and Y3= etc. and press CLEAR to remove all equations.
Next, press 2nd then STAT PLOT.
P ress 1 to select Plot 1, then Press ENTER to turn Plot 1 on. Note that Type, Xlist, Ylist, and Mark should all be set the same as the picture at the right. The Type shown is scattergram , the data list uses L 1 for the X- values, L 2 for the Y-values, and the points will be plotted as little squares as indicated by Mark.
Finally, to see the scattergram, press ZOOM, then press ZoomStat (9). ZoomStat automatically adjusts the calculator window so that all the points in the scattergram are visible.
III. Entering an equation
We use the top row of keys for graphing, they are:
Y= WINDOW ZOOM TRACE GRAPH
Start by pressing Y=. The flashing rectangle next to \Y1= is called the cursor. The cursor indicates where characters will appear when a key is pressed. If there are expressions next to any of the \Y= , use the to move the cursor to the line containing the expression and press CLEAR.
Now with the cursor at \Y1= enter 2 x + 5. Use the X,T, θ, n key to enter the variable x.
IV. Displaying Values in a Table
We can use a calculator to display a table of values for an equation that has been entered into the calculator. Press 2nd then TBLSET (the WINDOW button) to set up the table. TblStart is the first input value in the table and ∆ Tbl is the increment for the input values. Enter −2 for TblStart (be sure to use the (−) key) and press ENTER. Then enter 3 for ∆ Tbl and press ENTER.
Press 2nd then TABLE (the GRAPH button). Notice that the x values start at −2 and increase by an increment of 3. These are the instructions that you gave the calculator in the previous window. You can scroll up or down the table using or.
The cursor appears on one of the graphs. You can tell which one by looking at the upper left corner. The calculator prompts you to tell it which two graphs (curves) you are finding the intersection of. Press ENTER to indicate that the cursor is on one of your curves.
The cursor jumps to the other graph and prompts you with “Second curve?”. Press ENTER to indicate that the cursor is on the other curve.
Now the prompt is “Guess?”, which is asking you to place the cursor
near the point of intersection. Use the , and keys to move the
cursor close to the point of intersection.
Press ENTER. The cursor jumps to the point of intersection and the coordinates of that point are indicated along the bottom of the screen.
VII. Linear Regression
Using the data in the table at the right, we’ll use the calculator’s linear regression feature to find a linear equation that best fits the data. First, we need to enter the data into the stat lists. If you need to refresh your memory on how this is done, go to section II of this supplement and follow the first four steps of “Plotting Points in a Scattergram”.
x 2 5 8 11
y 25 28 58 130
When the data has been correctly entered your screen should look like the picture at the right.
To perform the linear regression function, first press the STAT key.
We want to perform a calculation on the data, so press the right arrow to CALC.
Select LinReg (4) to perform a linear regression. Note there are other types of regression besides linear. In this window the options include quadratic regression (QuadReg (6)) and exponential regression (ExpReg (0)) among others.
Press ENTER to perform the regression. This output describes a linear equation with slope 11.5 and y -intercept -14.5, so the equation is
y = 11.5 x − 14.5. We are not going to use the r^2 = or r = for our
purposes. Don’t worry if your calculator does not show these values.
To graph the regression equation along with the scattergram, first plot the scattergram by turning on plot 1 and pressing ZOOM then ZoomStat (9). If you need to refresh your memory on these steps, go to section II, “Plotting Points in a Scattergram”, and read steps 5 through
Press Y=. Be sure that all equations are cleared and the plot is turned on.
When we perform regression, the equation is stored as a statistics variable named RegEQ. We graph the regression equation by inserting RegEQ into the y= window. First, to find RegEQ, press the VARS key.
Since RegEQ is a statistics variable, select Statistics (5) by pressing 5.
RegEQ is an equation, so select EQ by pressing the right arrow twice
.
Select RegEQ by pressing 1 (or ENTER). This inserts the regression equation into the y= screen for graphing.
Guess? is a prompt for an x value in the specified range that the calculator can use to start its search algorithm. Any x -value in the range will work. If you press ENTER the calculator will use the x coordinate of the current position of the cursor. Since the cursor is at the right bound, that value is valid. Press ENTER. The cursor is flashing on the x -intercept and its coordinates are listed at the bottom of the screen: (−2,0).
Repeat the procedure to find the other x -intercept.
IX. Problems for Practice
Use a calculator to make a scattergram of each of the following data tables.
x 1 7 15 25
y 7 50 101 190
x 2 5 8 11
y 25 28 58 130
Use a calculator to make a table of values for the following equations. Use TblStart= − 10 and ∆ Tbl=
- y = 3 x + 2 4. y = 23 x + 4
Use a calculator to draw the graphs of the following equations.
- y = 3(2 − x ) 6. y = 5 + 2( x − 1)
- Use the “Intersect feature to solve the equation; 2 x − 3 = 4
- Find the point of intersection of the graphs of y^ =^ 5( x^ +^ 1)^ and y^ =^ −2( x^ +^ 3)
- Use linear regression to find a model of best fit (equation) for each of the tables. Graph the regression model and the scattergram in the same window. Round decimals to two places. a) b) x 1 7 15 25
y 7 50 101 190
x 2 5 8 11
y 25 28 58 130
- Find the x -intercepts of y = x^2 + 3. 9 x − 2. 7
Answers: (standard window)
x = 3.5, y = 4
- a) y = 7.55 x − 3.59 b) y = 11.5 x −14.
