ACTIVITY: Using a Table to Plot Points
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1 .5 Graphing Linear Equations in Standard Form equation a + b = c? How can ou describe the graph of the ACTIVITY: Using a Table to Plot Points Work with a partner. You sold a total of $6 worth of tickets to a school concert. You lost track of how man of each tpe of ticket ou sold. adult Number of adult tickets + student Number of student tickets = a. Let represent the number of adult tickets. Let represent the number of student tickets. Write an equation that relates and. b. Cop and complete the table showing the different combinations of tickets ou might have sold. Number of Adult Tickets, Number of Student Tickets, Graphing Equations In this lesson, ou will graph linear equations written in standard form. c. Plot the points from the table. Describe the pattern formed b the points. d. If ou remember how man adult tickets ou sold, can ou determine how man student tickets ou sold? Eplain our reasoning Chapter Graphing and Writing Linear Equations
2 ACTIVITY: Rewriting an Equation Work with a partner. You sold a total of $6 worth of cheese. You forgot how man pounds of each tpe of cheese ou sold. Pounds pound of swiss + Pounds of pound cheddar = Math Practice Understand Quantities What do the equation and the graph represent? How can ou use this information to solve the problem? a. Let represent the number of pounds of swiss cheese. Let represent the number of pounds of cheddar cheese. Write an equation that relates and. b. Rewrite the equation in slope-intercept form. Then graph the equation. c. You sold pounds of cheddar cheese. How man pounds of swiss cheese did ou sell? d. Does the value =.5 make sense in the contet of the problem? Eplain IN YOUR OWN WORDS How can ou describe the graph of the equation a + b = c?. Activities and show two different methods for graphing a + b = c. Describe the two methods. Which method do ou prefer? Eplain. 5. Write a real-life problem that is similar to those shown in Activities and. 6. Wh do ou think it might be easier to graph + = 0 without rewriting it in slope-intercept form and then graphing? Use what ou learned about graphing linear equations in standard form to complete Eercises and on page 600. Section.5 Graphing Linear Equations in Standard Form 597
3 .5 Lesson Lesson Tutorials Ke Vocabular standard form, p. 598 Stud Tip An linear equation can be written in standard form. Standard Form of a Linear Equation The standard form of a linear equation is a + b = c where a and b are not both zero. EXAMPLE Graphing a Linear Equation in Standard Form Graph + = 6. Step : Write the equation in slope-intercept form. + = 6 = 6 Write the equation. Add to each side. = Divide each side b. Step : Use the slope and the -intercept to graph the equation. slope = + ( ) -intercept Check (0, ) Use the slope to plot another point, (, 0). 6 6 The -intercept is. So, plot (0, ). 6 Draw a line through the points. Eercises 5 0 Graph the linear equation. Use a graphing calculator to check our graph.. + =. + = 6. + = 0. + = Chapter Graphing and Writing Linear Equations
4 EXAMPLE Graphing a Linear Equation in Standard Form Graph + = using intercepts. Step : To find the -intercept, To find the -intercept, substitute 0 for. substitute 0 for. + = + = + (0) = 0 + = = = Step : Graph the equation. Check 6 The -intercept is. So, plot (, 0). (, 0) (0, ) 5 6 The -intercept is. So, plot (0, ). Draw a line through the points. EXAMPLE Real-Life Application You have $6 to spend on apples and bananas. (a) Graph the equation = 6, where is the number of pounds of apples and is the number of pounds of bananas. (b) Interpret the intercepts. a. Find the intercepts and graph the equation. -intercept -intercept = = (0) = 6.5(0) = 6 = = 0 (0, 0) b. The -intercept shows that ou can bu pounds of apples when ou do not bu an bananas. The -intercept shows that ou can bu 0 pounds of bananas when ou do not bu an apples (, 0) Eercises 6 8 Graph the linear equation using intercepts. Use a graphing calculator to check our graph. 5. = = 6 7. WHAT IF? In Eample, ou bu pounds of oranges instead of bananas. Oranges cost $.0 per pound. Graph the equation.5 +. = 6. Interpret the intercepts. Section.5 Graphing Linear Equations in Standard Form 599
5 .5 Eercises Help with Homework. VOCABULARY Is the equation = + 5 in standard form? Eplain.. WRITING Describe two was to graph the equation + = 6. 9+(-6)= +(-)= +(-9)= 9+(-)= Define two variables for the verbal model. Write an equation in slope-intercept form that relates the variables. Graph the equation.. $.00 pound Pounds of peaches + $.50 pound Pounds of apples = $5. 6 miles Hours hour biked + miles Hours hour walked = miles Write the linear equation in slope-intercept form = = 7. + = 0 Graph the linear equation. Use a graphing calculator to check our graph = = 0. + = Match the equation with its graph.. 5 = = = 0 A. 5 5 B. 5 5 C ERROR ANALYSIS Describe and correct the error in finding the -intercept. 5. BRACELET A charm bracelet costs $65, plus $5 for each charm. The equation 5 + = 65 represents the cost of the bracelet, where is the number of charms. a. Graph the equation. b. How much does the bracelet shown cost? + = (0) + = = = 600 Chapter Graphing and Writing Linear Equations
6 Graph the linear equation using intercepts. Use a graphing calculator to check our graph. 6. = 7. + = = 9. SHOPPING The amount of mone ou spend on CDs and DVDs is given b the equation + 8 = 6. Find the intercepts and graph the equation. Boat: $ 50/da Gear: $ 50/da 0. SCUBA Five friends go scuba diving. The rent a boat for das and scuba gear for das. The total spent is $000. a. Write an equation in standard form that represents the situation. b. Graph the equation and interpret the intercepts.. MODELING You work at a restaurant as a host and a server. You earn $9.5 for each hour ou work as a host and $7.65 for each hour ou work as a server. a. Write an equation in standard form that models our earnings. b. Graph the equation. Basic Information Pa to the Order of:... John Doe # of hours worked as... host: # of hours worked as... server: Earnings for this pa... period: $ LOGIC Does the graph of ever linear equation have an -intercept? Eplain our reasoning. Include an eample.. For a house call, a veterinarian charges $70, plus $0 an hour. a. Write an equation that represents the total fee (in dollars) the veterinarian charges for a visit lasting hours. b. Find the -intercept. Does this value make sense in this contet? Eplain our reasoning. c. Graph the equation. The points in the table lie on a line. Find the slope of the line. (Section.) MULTIPLE CHOICE Which value of makes the equation = 9 true? (Topic ) A B 0 C D Section.5 Graphing Linear Equations in Standard Form 60
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