Graphs of the Linear Function: Graphing Calculator TI-84 Plus

Presented by Victor Zinger

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Table of Contents• Welcome• TI-84 Plus Keyboard• Dimensions of the screen• Exploring Y-screen and Table of values• Exploring Y-screen and Table of values(continue)• Example # 1• Solving Linear Equations Graphically• Example # 2• Linear Inequalities• Problem Solving Strategy• Applications of Linear Function: Line of the Best Fit• Line of the Best Fit• Thank You!

Welcome

• My name is Victor Zinger. I am Professor of Mathematics at the University of Alaska Fairbanks. Mathematics is important for everyone’s career and success in their lives. Mathematics is language for all-let’s make it understandable!

TI-84 Plus Keyboard• Lower center (white keys):

Arithmetic Keys • Lower Right (gray keys):

Basic Operations • Lower Left (black keys):

Basic Functions • Top Row: (gray keys):

Display Keys • Next Three Rows:

Special Program Keys • Middle Row: (black keys):

Trig. and Inverse Trig. Functions

Dimensions of the screen

Press the WINDOW key (top row) to see the Window Screen shown to the right: This shows that the dimensions of the graphing window are: -4.7 < x < 4.7 and -3.1 < y < 3.1 Also, the tick marks are spaced by 1 unit on each axis. Using the ARROW keys to move the blinking cursor, change the screen dimensions to: -1 < x < 5 and -2 < y < 10

Exploring Y-screen and Table of values•Use the MODE key to select the "Func" mode of function entry. •Use the Y= key to select (or enter fresh) for example function: Y2=2x+1 •Press the 2nd key, then the WINDOW key (= Tblset). •Edit the Table Setup Window as shown to the right.

Video clip

Exploring Y-screen and Table of valuesPress the 2nd key then the GRAPH key (= TABLE key) to see the table of values to the right. These are the values of the functions y1=3x*2^(-x) and y2=2x+1. Use the Up and Down ARROWS to scroll through the values. Press the 2nd key, then the WINDOW key (= Tblset). Note that the TblMin value is the the topmost x-value displayed on the table. Edit the Table Setup values to TblMin=-2 and (delta)Tbl=1. Press 2nd then GRAPH. .

Example # 1Solving a system of linear equations:

32

1

72

xy

xy

TI-84 Plus:1. Press "Y="2. Enter both equations, solved for Y3. Press "GRAPH"4. If all intersection points are not visible, press "ZOOM" then 0 or select "0: ZoomFit"5. Press "2nd" then "TRACE"6. Press 5 or select "5: intersect"7. Move the cursor to one of the intersection points. (There may be only one) Each of these points represents one solution to the system.8. Press "ENTER" three times9. The coordinates of the intersection are shown at the bottom of the screen

Solving Linear Equations Graphically

STEP 1: Set Y1 equal to the left side of the equation and set equal to the right side of the equation. STEP 2: Graph Y1 and Y2 in the same viewing rectangle. STEP 3: Locate any points of intersection. The x-values of these points correspond to the solutions to the equation.

STEP 4: Press 2nd TRACE[CALC], then press 5 to select intersect.

Solve the equation: 10000 = 214.2 (x – 1950) + 2322

TI -84 Tutorial

Example # 2

Instruction: Notice the "shade below" symbol to the far left of the Y1. Again, you must determine whether to draw a solid or dotted line.  This problem uses a dotted line because it is strictly "less than" (no "equal to").

Solve linear inequality

33 xy

Linear Inequalities

Enter 2x + 1 into Y1

Arrow to the far left side of Y1 Press ENTER until the "shade above" symbol is displayed. Press ZOOM #6 ZStandard (for a 10x10 window) Graph NOTE:  You will have to determine whether to draw a solid line or a dotted line for  y = 2x + 1.  This problem uses a solid line because of the "less than or equal to" sign.  The calculator will display a solid line at all times.

Graph

12 xy

12 xy

Problem Solving Strategy

Algebraic Problem

Applications of Linear Function: Line of the Best Fit

Link to Tutorial

Problem: “Maximum Heart Rate” A person who is exercising should not exceed his or her maximum heart rate, which is determined on the basis of that person’s sex, age, and resting heart rate. The following table relates resting heart rate and maximum heart rate for a 20-year-old man. Use a graphing calculator to model the data with a linear function.

Resting Heart Rate, H (In Beats Per Minute

Maximum Heart Rate, M (In Beats Per Minute

50 166

60 168

70 170

80 172

Line of the Best Fit

Thank You and Good Luck!