ACTIVITY: Graphing a Linear Equation. 2 x x + 1?
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1 . Graphing Linear Equations How can ou draw its graph? How can ou recognize a linear equation? ACTIVITY: Graphing a Linear Equation Work with a partner. a. Use the equation = + to complete the table. (Choose an two -values and find the -values.) b. Write the two ordered pairs given b the table. These are called solution points of the equation. c. PRECISION Plot the two solution points. Draw a line eactl through the two points. d. Find a different point on the line. Check that this point is a solution point of the equation = +. e. LOGIC Do ou think it is true that an point on the line is a solution = Solution Points 6 5 O point of the equation = +? Eplain. f. Choose five additional -values for the table. (Choose positive and negative -values.) Plot the five corresponding solution points. Does each point lie on the line? COMMON CORE Graphing Equations In this lesson, ou will understand that lines represent solutions of linear equations. graph linear equations. Learning Standards A.CED. A.REI.0 = + Solution Points g. LOGIC Do ou think it is true that an solution point of the equation = + is a point on the line? Eplain. h. THE MEANING OF A WORD Wh is = a + b called a linear equation? Chapter Graphing and Writing Linear Equations
2 ACTIVITY: Using a Graphing Calculator Math Practice Recognize Usefulness of Tools What are some advantages and disadvantages of using a graphing calculator to graph a linear equation? Use a graphing calculator to graph = + 5. a. Enter the equation = + 5 into our calculator. b. Check the settings of the viewing window. The boundaries of the graph are set b the minimum and maimum - and -values. The number of units between the tick marks are set b the - and -scales. This is the standard viewing window. c. Graph = + 5 on our calculator d. Change the settings of the viewing window to match those shown. 5 8 Compare the two graphs. 6. IN YOUR OWN WORDS How can ou recognize a linear equation? How can ou draw its graph? Write an equation that is linear. Write an equation that is not linear.. Use a graphing calculator to graph = 5 in the standard viewing window. a. Can ou tell where the line crosses the -ais? Can ou tell where the line crosses the -ais? b. How can ou adjust the viewing window so that ou can determine where the line crosses the - and -aes? 5. CHOOSE TOOLS You want to graph =.5.8. Would ou graph it b hand or using a graphing calculator? Wh? Use what ou learned about graphing linear equations to complete Eercises and on page 6. Section. Graphing Linear Equations
3 . Lesson Lesson Tutorials Ke Vocabular linear equation, p. solution of a linear equation, p. Remember An ordered pair (, ) is used to locate a point in a coordinate plane. Linear Equations A linear equation is an equation whose graph is a line. The points on the line are solutions of the equation. You can use a graph to show the solutions of a linear equation. The graph below is for the equation = +. (, ) 0 (, 0) 0 (0, ) (, ) (, 0) = + (0, ) (, ) EXAMPLE Graphing a Linear Equation Graph = +. Step : Make a table of values. Check = + (, ) = ( ) + (, ) 0 = (0) + (0, ) = () + (, ) (, ) = + (0, ) Step : Plot the ordered pairs. Step : Draw a line through the points. (, ) Graphing Horizontal and Vertical Lines The graph of = b is a horizontal line passing through (0, b). The graph of = a is a vertical line passing through (a, 0). b (0, b) O a (a, 0) O Chapter Graphing and Writing Linear Equations
4 EXAMPLE Graphing a Horizontal Line and a Vertical Line a. Graph =. b. Graph =. The graph of = is a horizontal line passing through (0, ). Draw a horizontal line through this point. The graph of = is a vertical line passing through (, 0). Draw a vertical line through this point. O (0, ) (, 0) O Eercises 5 6 Graph the linear equation. Use a graphing calculator to check our graph, if possible.. =. = +. =. =.5 EXAMPLE Real-Life Application The wind speed (in miles per hour) of a tropical storm is = + 66, where is the number of hours after the storm enters the Gulf of Meico. a. Graph the equation. b. When does the storm become a hurricane? a. Make a table of values. = + 66 (, ) 0 = (0) (0, 66) 76 = + 66 = () (, 68) 7 A tropical storm becomes a hurricane when wind speeds are at least 7 miles per hour. = () (, 70) = () (, 7) 68 6 Plot the ordered pairs and draw a line through the points b. From the graph, ou can see that = 7 when =. So, the storm becomes a hurricane hours after it enters the Gulf of Meico. 5. WHAT IF? In Eample, the wind speed of the storm is = When does the storm become a hurricane? Section. Graphing Linear Equations 5
5 . Eercises Help with Homework. VOCABULARY What tpe of graph represents the solutions of the equation = +?. WHICH ONE DOESN T BELONG? Which equation does not belong with the other three? Eplain our reasoning. = = = = 9+(-6)= +(-)= +(-9)= 9+(-)= PRECISION Cop and complete the table. Plot the two solution points and draw a line eactl through the two points. Find a different solution point on the line... = = + Graph the linear equation. Use a graphing calculator to check our graph, if possible. 5. = 5 6. = 7. = 5 8. = 6 9. = 0. = 7. = +. =. =. = = = 7. ERROR ANALYSIS Describe and correct the error in graphing the equation. 8. MESSAGING You sign up for an unlimited tet messaging plan for our cell phone. The equation = 0 represents the cost (in dollars) for sending tet messages. Graph the equation. What does the graph tell ou? O = (, 0) 9. MAIL The equation = + represents the cost (in dollars) of mailing a package that weighs pounds. a. Graph the equation. b. Use the graph to estimate how much it costs to mail the package. c. Use the equation to find eactl how much it costs to mail the package. 6 Chapter Graphing and Writing Linear Equations
6 Solve for. Then graph the equation. Use a graphing calculator to check our graph. 0. =. 5 + =. + = =.5. SAVINGS You have $00 in our savings account and plan to deposit $.50 each month. a. Write and graph a linear equation that represents the balance in our account. b. How man months will it take ou to save enough mone to bu 0 acres of land on Mars? Video time: min. 0 sec. 5. CAMERA One second of video on our digital camera uses the same amount of memor as two pictures. Your camera can store 50 pictures. a. Write and graph a linear equation that represents the number of pictures our camera can store if ou take seconds of video. b. How man pictures can our camera store after ou take the video shown? 6. PROBLEM SOLVING Along the U.S. Atlantic Coast, the sea level is rising about millimeters per ear. How man millimeters has sea level risen since ou were born? How do ou know? Use a linear equation and a graph to justif our answer. 7. The sum S of the measures of the angles of a polgon is S = (n ) 80, where n is the number of sides of the polgon. a. Plot four points (n, S ) that satisf the equation. Do the points lie on a line? Eplain our reasoning. b. Does the value n =.5 make sense in the contet of the problem? Eplain our reasoning. Write the ordered pair corresponding to the point. (Skills Review Handbook) B 6 8. Point A 9. Point B A 0. Point C. Point D. MULTIPLE CHOICE A debate team has 5 female members. The ratio of females to males is :. How man males are on the debate team? (Skills Review Handbook) 6 O A 6 B 0 C D 5 D C Section. Graphing Linear Equations 7
ACTIVITY: Graphing a Linear Equation. 2 x x + 1?
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