using the ti 83 84

Using the TI Graphing Calculator

“Using the TI 83 84 Graphing Calculator”About 55,200 results

Contents• Graphing an Equation• Graphing Systems of Linear Equations• Graphing Linear Inequalities• Calculating Correlation Coefficient• Finding a Regression Equation

Graphing Equations Using a TI-83/84:

Step 1: Press [Y=] and key in the equation using [X, T, Θ, n] for x.

Step 2: Press [WINDOW] to change the viewing window, if necessary.

Step 3: Enter in appropriate values for Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl, using the arrow keys to navigate.

Step 4: Press [GRAPH].

1.3.1: Creating and Graphing Linear Equations in Two Variables

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Example 1A Boeing 747 starts out a long flight with about 57,260 gallons of fuel in its tank. The airplane uses an average of 5 gallons of fuel per mile. Write an equation that models the amount of fuel in the tank and then graph the equation using a graphing calculator.

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Example 1, continued

Substitute the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y-intercept.

m = 5b = 57,260y = –5x + 57,260

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Graph the equation on your calculator.On a TI-83/84:

Step 1: Press [Y=].Step 2: At Y1, type in [(–)][5][X, T, Θ, n][+]

[57260].Step 3: Press [WINDOW] to change the viewing

window.Step 4: At Xmin, enter [0] and arrow down 1

level to Xmax.Step 5: At Xmax, enter [3000] and arrow down 1

level to Xscl.


Redraw the graph on graph paper.On the TI-83/84, the scale was entered in [WINDOW] settings. The X scale was 100 and the Y scale was 1,000. Set up the graph paper using these scales. Label the y-axis “Fuel used in gallons.” Show a break in the graph from 0 to 40,000 using a zigzag line. Label the x-axis “Distance in miles.” To show the table on the calculator so you can plot points, press [2nd][GRAPH]. The table shows two columns with values; the first column holds the x-values, and the second column holds the y-values.


Pick a pair to plot, and then connect the line. To return to the graph, press [GRAPH]. Remember to label the line with the equation.

(Note: It may take you a few tries to get the window settings the way you want. The graph that follows shows an X scale of 200 so that you can easily see the full extent of the graphed line.)

Guided Practice: Example 1, continued

Example 2An investment of $500 is compounded monthly at a rate of 3%. What is the equation that models this situation? Graph the equation.


Read the problem statement and then reread the scenario, identifying the known quantities.

Initial investment = $500r = 3%Compounded monthly = 12 times a year


Substitute the known quantities into the general form of the compound interest formula.

In this formula, , P is the initial value, r is

the interest rate, n is the number of times the

investment is compounded in a year, and t is the

number of years the investment is left in the account

to grow.

Example 2, continuedP = 500r = 3% = 0.03n = 12


Notice that, after simplifying, this form is similar to

y = abx. To graph on the x- and y-axes, put the

compounded interest formula into this form, in which

A = y, P = a, , and t = x.

A = 500(1.0025)12t becomes y = 500(1.0025)12x.


Graph the equation using a graphing calculator.

On a TI-83/84:Step 1: Press [Y=].Step 2: Type in the equation as follows:

[500][×][1.0025][^][12][X, T, Θ, n]Step 3: Press [WINDOW] to change the

viewing window.Step 4: At Xmin, enter [0] and arrow down

1 level to Xmax.Step 5: At Xmax, enter [10] and arrow

down 1 level to Xscl.


Step 6: At Xscl, enter [1] and arrow down 1 level to Ymin.

Step 7: At Ymin, enter [500] and arrow down 1 level to Ymax.

Step 8: At Ymax, enter [700] and arrow down 1 level to Yscl.

Step 9: At Yscl, enter [15].Step 10: Press [GRAPH].


Transfer your graph from the screen to graph paper.

Use the same scales that you set for your viewing window.The x-axis scale goes from 0 to 10 years in increments of 1 year.The y-axis scale goes from $500 to $700 in increments of $15. You’ll need to show a break in the graph from 0 to 500 with a zigzag line, as shown in the graph that follows.


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Example 3

Create a table of values for the exponential function

. Identify the asymptote and y-intercept of

the function. Plot the points and sketch the graph of the

function, and describe the end behavior.

Example 3, continuedCreate a table of values.

Choose values of x and solve for the corresponding values of f(x).

x f(x)–4 17.25–2 60 12 –1.224 –2.2099

Example 3, continuedIdentify the asymptote of the function.

The asymptote of the function is always the constant, k.

In the function , the value of

k is –3.

The asymptote of the function is y = –3.

Example 3, continuedDetermine the y-intercept of the function.

The y-intercept of the function is the value of f(x) when x is equal to 0.

It can be seen in the table that when x = 0, f(x) = 1.

The y-intercept is (0, 1).

Example 3, continuedGraph the function.

Use the table of values to create a graph of the function.

Example 3, continuedDescribe the end behavior of the graph.

The end behavior is what happens at the ends of the graph.

As x becomes larger, the value of the function approaches the asymptote, –3.

As x becomes smaller, the value of the function approaches infinity.

Since the function approaches infinity as x becomes smaller, the graph shows exponential decay.

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Example 4You deposit $100 into a long-term certificate of deposit (CD) in which your money will double every 7 years.

1. Write a function to show how much money you will have in total in 7, 14, 21, 28, and 35 years.

2. Use the function to create a table 3. Graph the function. 4. What do the parameters represent in the context of

this problem?

Example 4, continuedWrite a function.

This scenario is represented by an exponential function. • The initial deposit is $100. • Your money doubles every 7 years, so the growth factor is 2.• The time period is 7 years.

Substitute these values into the exponential function.

The function for this scenario is .

Example 4, continuedCreate a table.

Let x = the number of years and f(x) = the amount of money in dollars.

Use the values 7, 14, 21, 28, and 35 for x.


x f(x)

7 200

14 400

21 800

28 1600

35 3200

Example 4, continuedGraph the function.

Use the table of values to plot the function.

Example 4, continuedIdentify the parameters.

The parameters in this problem are the starting amount of $100 and the growth rate of 2.

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Graphing Systems of Equations Using a TI-83/84:Step 1: Press [Y=] and key in the equation using

[X, T, Θ, n] for x.Step 2: Press [ENTER] and key in the second equation.Step 3: Press [WINDOW] to change the viewing window, if

necessary.Step 4: Enter in appropriate values for Xmin, Xmax, Xscl,

Ymin, Ymax, and Yscl, using the arrow keys to navigate.

Step 5: Press [GRAPH].Step 6: Press [2ND] and [TRACE] to access the Calculate

Menu.Step 7: Choose 5: intersect.Step 8: Press [ENTER] 3 times for the point of intersection.

Example 5

Solve the system: y = -2x + 9 and y = 3x - 4

1. Enter the first equation into Y1. 2. Enter the second equation into Y2. 3. Hit GRAPH. 4. Use the INTERSECT option to find where the two graphs intersect (the answer). 2nd TRACE (CALC) #5 intersect Move spider close to the intersection. Hit ENTER 3 times.

5. Answer: x = 2.6 and y = 3.8

Let’s do another one.Example 6

Graphing Linear Inequalities Using a TI-83/84:

Step 1: Press [Y=] and arrow over to the left two times so that the cursor is blinking on the “\”.

Step 2: Press [ENTER] two times for the greater than icon “ ” and three times for the less than icon “ ”.

Step 3: Arrow over to the right two times so that the cursor is blinking after the equal sign.

Step 4: Key in the equation using [X, T, Θ, n] for x.Step 5: Press [WINDOW] to change the viewing window, if

necessary.Step 6: Enter in appropriate values for Xmin, Xmax, Xscl, Ymin,

Ymax, and Yscl, using the arrow keys to navigate.Step 7: Press [GRAPH].

Example

Example 7

Calculating and Interpreting the Correlation CoefficientThe correlation coefficient, r, is a quantity that allows us to determine how strong this relationship is between two events. It is a value that ranges from –1 to 1; a correlation coefficient of –1 indicates a strong negative correlation, a correlation coefficient of 1 indicates a strong positive correlation, and a correlation coefficient of 0 indicates a very weak or no linear correlation. Note that a correlation between two events does not imply that changing one event causes a change in the other event—only that a change might have taken place in the other event. This will be explored more later.

Continued

Continued

n X X2 Y Y2 XY

1 2 32 4 43 6 74 8 65 10 9Σ

Key Concepts, continued

On a TI-83/84:You can use a calculator to calculate the correlation coefficient.

Step 1: Set up the calculator to find correlations. Press [2nd], then [CATALOG] (the “0” key). Scroll down and select DiagnosticOn, then press [ENTER]. (This step only needs to be completed once; the calculator will stay in this mode until changed in this menu.)

Step 2: To calculate the correlation coefficient, first enter the data into a list. Press [2nd], then L1 (the “1” key). Scroll to enter data sets. Press [2nd], then L2 (the “2” key). Enter the second event in L2.

Step 3: Calculate the correlation coefficient. Press [STAT], then select CALC at the top of the screen. Scroll down to 8:LinReg(a+bx), and press [ENTER].

The r value (the correlation coefficient) is displayed along with the equation.

X Y

2 34 46 78 6

10 9

Example 9: Andrew wants to estimate his gas mileage, or miles traveled per gallon of gas used. He records the number of gallons of gas he purchased and the total miles he traveled with that gas.

What is the correlation between the number of gallons purchased and the total milesHe traveled?

Gallons Miles15 31317 34018 40119 42318 39217 37920 40819 43716 36620 416

Example 9, continuedCreate a scatter plot of the data.

Let the x-axis represent the number of gallons purchased and the y-axis represent the miles traveled.

Mile

s

Gallons

Example 9, continuedAnalyze the scatter plot, and describe any relationship between the two events.

As the number of gallons increases, the miles also increase. The shape of the graph is approximately a line, and it appears there is a positive linear correlation between gallons and miles.

Example 9, continuedFind the correlation coefficient using a graphing calculator. Follow the steps in the Key Concepts section.

r = 0.872

Example 9, continuedDescribe the correlation between the two events.

0.872 is close to 1. There is a strong positive linear correlation between the gallons purchased and the miles traveled.

Find a Regression Equation• A graphing calculator can graph a scatter plot of given data and find a

regression equation that models the given data. • Begin by entering the data into lists on your calculator, as outlined in the

following steps. • Decide whether the data would best be modeled with a quadratic

regression, linear regression, or exponential regression. (In this lesson, we focus on quadratic regressions, but you can choose the type of regression that is most appropriate for the situation.)

• To decide which regression model is best, look at the scatter plot of the data you entered.

• After you find the appropriate model using your calculator, you can graph this equation on top of the scatter plot to verify that it is a reasonable model.

Example 10: Linear RegressionAndrew wants to estimate his gas mileage, or miles traveled per gallon of gas used. He records the number of gallons of gas he purchased and the total miles he traveled with that gas.

Use your calculator to make a scatter plot of the data in the table and to find a linear regression of this data.

Gallons Miles15 31317 34018 40119 42318 39217 37920 40819 43716 36620 416

Example 10 continuedCreate a scatter plot showing the relationship between gallons of gas and miles driven.

Gallons Miles15 31317 34018 40119 42318 39217 37920 40819 43716 36620 416

Step 1: Press [STAT]. Step 2: Press [ENTER] to select Edit. Step 3: Enter x-values into L1. Step 4: Enter y-values into L2.Step 5: Press [2nd][Y=]. Step 6: Press [ENTER] to turn on Stat Plot, Step 7: For Plot 1, press [ENTER] to turn on; scroll down to TYPE select type scatter plot. (optional: select lists and MARK).Step 7: Press [ZOOM][9] to select ZoomStat and show the scatter plot.

Example 10, continuedPlot each point on the coordinate plane.

Let the x-axis represent gallons and the y-axis represent miles.

Mile

s

Gallons

Gallons Miles15 31317 34018 401

19 42318 39217 379

20 40819 43716 36620 416

Example 10, continued• Your graphing calculator can help you to find a linear regression model

after you input the data.

Entering Lists Using a TI-83/84:

Step 1: Press [STAT]. Step 2: Arrow to the right to select Calc. Step 3: Press [5] to select LinReg. Step 4: At the LinReg (a + bx) screen, Press [ENTER]

y = a + bxa = 24.10843373b = 20. 30120482

Step 5: Press [y=] and enter regression equation y = 20.3x + 24.1Step 6: Press [GRAPH]

Example 10, continuedGraph the line of best fit.

Mile

s

Gallons

Gallons Miles15 31317 34018 401

19 42318 39217 379

20 40819 43716 36620 416

Example 11The students in Ms. Swan’s class surveyed people of all ages to find out how many people in each of several age groups exercise on a regular basis. Their data is shown in the table on the next slide. Use your calculator to make a scatter plot of the data in the table and to find a quadratic regression of this data. Use the “Group number” column in the table to represent the age group, the x-values. Graph the regression equation on top of your scatter plot.


Age range 11–20 21–30 31–40 41–50 51–60 61–70Group number (x) 1 2 3 4 5 6

Number of people who exercise (y)

21 38 43 41 26 11

Example 11, continuedMake a scatter plot of the data.

On a TI-83/84: Step 1: Press [STAT]. Step 2: Press [ENTER] to select Edit. Step 3: Enter x-values into L1. Step 4: Enter y-values into L2. Step 5: Press [2nd][Y=]. Step 6: Press [ENTER] twice to turn on the Stat Plot. Step 7: Press [ZOOM][9] to select ZoomStat and

show the scatter plot.

Example 11, continuedFind the quadratic regression model that best fits this data.

On a TI-83/84: Step 1: Press [STAT].Step 2: Arrow to the right to select Calc.Step 3: Press [5] to select QuadReg.Step 4: At the QuadReg screen, enter the parameters for the

function (Xlist: L1, Ylist: L2, Store RegEQ: Y1). To enter Y1, press [VARS] and arrow over to the right to “Y-VARS.” Select 1: Function. Select 1: Y1.

Step 5: Press [ENTER] twice to see the quadratic regression equation.

Step 6: Press [ZOOM][9] to view the graph of the scatter plot and the regression equation.

Example 11, continuedA quadratic regression model for this problem is

y = –4.286x2 + 27.486x – 1.2.

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Example 12Doctors recommend that most people exercise for 30 minutes every day to stay healthy. To get the best results, a person’s heart rate while exercising should reach between 50% and 75% of his or her maximum heart rate, which is usually found by subtracting your age from 220. The peak rate should occur at around the 25th minute of exercise. Alice is 30 years old, and her maximum heart rate is 190 beats per minute (bpm). Assume that her resting rate is 60 bpm.

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5.9.2: Fitting a Function to Data

Example 12, continuedThe table below shows Alice’s heart rate as it is measured every 5 minutes for 30 minutes while she exercises. Interpret the model.

Make a scatter plot of the data. Use a graphing calculator to find a quadratic regression model for the data. Use your model to extrapolate Alice’s heart rate after 35 minutes of exercise.

Time (minutes) 0 5 10 15 20 25 30Heart rate (bpm) 60 93 113 134 142 152 148

Example 12, continuedMake a scatter plot of the data.

On a TI-83/84: Step 1: Press [STAT].Step 2: Press [ENTER] to select Edit.Step 3: Enter x-values into L1.Step 4: Enter y-values into L2.Step 5: Press [2nd][Y=].Step 6: Press [ENTER] twice to turn on the Stat Plot.Step 7: Press [ZOOM][9] to select ZoomStat and

show the scatter plot.

Example 12, continuedFind a quadratic regression model using your graphing calculator.

On a TI-83/84: Step 1: Press [STAT].Step 2: Arrow to the right to select Calc.Step 3: Press [5] to select QuadReg.Step 4: At the QuadReg screen, enter the parameters

for the function (Xlist: L1, Ylist: L2, Store RegEQ: Y1). To enter Y1, press [VARS] and arrow over to the right to “Y-VARS.” Select 1: Function. Select 1: Y1.

Step 5: Press [ENTER] twice to see the quadratic regression equation.

Step 6: Press [ZOOM][9] to view the graph of the scatter plot and the regression equation

Example 12, continuedA quadratic regression model for this problem is y = –0.1243x2 + 6.6643x + 60.7143.

Example 12, continuedUse your model to extrapolate Alice’s heart rate after 35 minutes of exercise.

Substitute 35 for x in the regression model. y = –0.1243(35)2 + 6.6643(35) + 60.7143 y ≈ 141.70

After 35 minutes of exercise, we can expect Alice’s heart rate to be approximately 141.7 beats per minute.

Example 12, continuedInterpret the model.

Alice appears to be reducing her heart rate and, therefore, reducing her exercise intensity after a peak at approximately 27 minutes. If she continues the trend, her heart rate will be back to her resting heart rate at approximately 54 minutes. Heart rates below her resting heart rate can be ignored.

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using the ti 83 84

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