Standard Form. Check Skills You ll Need (For help, go to Lessons 2-3 and 2-6.) Solve each equation for y.

Transcription

1 -. Plan Lesson Preview heck Skills You ll Need Solving Multi-Step Equations Lesson -: Eample Eercises 0 Etra Practice, p. 70 Formulas Lesson -: Eample Eercises 9 Etra Practice, p. 70 Lesson Resources Teaching Resources Practice, Reteaching, Enrichment heckpoint Quiz Reaching ll Students Practice Workbook - Spanish Practice Workbook - Reading and Math Literac Spanish Reading & Literac Spanish heckpoint Quiz asic lgebra Planning Guide - Presentation ssistant Plus! Transparencies heck Skills You ll Need - dditional Eamples - Student Edition nswers - Lesson Quiz - PH Presentation Pro D - heckpoint Quiz omputer Test Generator D Technolog Resource Pro D-RM omputer Test Generator D Prentice Hall Presentation Pro D Student Site Teacher Web ode: aek-00 Graphing alculator, Procedure Self-grading Lesson Quiz Teacher enter Lesson Planner Resources Plus 9 Lesson Preview What You ll Learn JETIVE JETIVE - To graph equations using intercepts To write equations in standard form... nd Wh To use an equation to model a real-world situation that involves eercise, as in Eample Standard Form 9 hapter Linear Equations and Their Graphs heck Skills You ll Need (For help, go to Lessons - and -.) Solve each equation for. Part Graphing Graphing Equations Equations Using Intercepts JETIVE. nswers ma var. Sample: = ±. - = 0 ± 0. - =. 0 + =. 9 + =. - = ± ± ± lear each equation of decimals = = = ± New Vocabular standard form of a linear equation -intercept Investigation: Intercepts Interactive lesson includes instant self-check, tutorials, and activities.. Make a table of values for the equation - =. See left.. Use the table of values to graph - =. See left.. What is the -intercept?. What is the value of when the line crosses the -ais?. In the equation - =, what is the value of when = 0? What is the value of when = 0? ;. Using our answers to,, and, eplain how ou can make a graph of - = without making a table. nswers ma var. Sample: Find - and -intercepts, and then connect the two points. The slope-intercept form is just one form of a linear equation. nother form is standard form, which is useful in making quick graphs. Ke oncepts Definition Standard Form of a Linear Equation efore the Lesson Diagnose prerequisite skills using: heck Skills You ll Need The standard form of a linear equation is + =, where,, and are real numbers, and and are not both zero. You can use the - and -intercepts to make a graph. The -intercept is the -coordinate of the point where a line crosses the -ais. To graph a linear equation in standard form, ou can find the -intercept b substituting 0 for and solving for. Similarl, to find the -intercept, substitute 0 for and solve for. ngoing ssessment and Intervention During the Lesson Monitor progress using: heck Understanding dditional Eamples Standardized Test Prep fter the Lesson ssess knowledge using: Lesson Quiz omputer Test Generator D hapter heckpoint (p. 0)

2 heck Understanding Finding - and -Intercepts Find the - and -intercept of + =. Step To find the -intercept, Step To find the -intercept, substitute 0 for and solve for. substitute 0 for and solve for. + = + = + (0) = (0) + = = = = = The -intercept is The -intercept is.. Find the - and -intercepts of - 9 =-. ;. Teach Math ackground François Viète, a French mathematician of the siteenth centur, was the first to use letters as coefficients before variables. He also he introduced the + and - signs, although he never used the = sign. JETIVE Teaching Notes. heck Understanding Need Help? The slope of a horizontal line is 0, and the slope of a vertical line is undefined. If the - and -intercepts are integers, ou can use them to make a quick graph. Graphing Lines Using Intercepts Graph + = using intercepts. Step Find the intercepts. Step Plot (0, ) and (, 0). + = Draw a line through the points. + (0) = Substitute 0 for. = Solve for. = (0) + = Substitute 0 for. = Solve for. = Graph + =-0 using the - and -intercepts. See left. In the standard form of an equation + =, either or, but not both, ma be zero. If or is zero, the line is either horizontal or vertical. Graphing Horizontal and Vertical Lines a. Graph =-. b. Graph =. 0 + =- d Write in standard form. S + 0 = For all values of, =-. For all values of, =. Investigation (ptional) Suggest that students rewrite the equation as = + to make a table of values. Since the values substituted for are divided b, suggest students choose onl multiples of for. Tactile Learners To find the -intercept, have students cover the term with a finger, then solve the remaining equation for. Repeat to find the -intercept b covering the term. sk students wh this works. overing the term represents the 0 value of the term when 0 is substituted for the variable. dditional Eamples Find the - and -intercepts of + =., Graph + = using intercepts. heck Understanding Graph each equation. a d. See back of book. a. = b. = 0 c. =- d. = 0 Lesson - Standard Form 99 Reaching ll Students elow Level Students ma confuse the coefficients of and with the - and - intercepts. Use the linear equation in Eample to illustrate the difference. dvanced Learners hallenge students to develop the equations for horizontal lines and for vertical lines from the standard form + =. Tactile Learners See note on page 99. Diversit See note on page

3 dditional Eamples a. Graph =. b. Graph =-. JETIVE Part Writing Equations in Standard Form heck Understanding You can change an equation from slope-intercept form to standard form. If the equation contains fractions or decimals, multipl to write the equation using integers. Transforming to Standard Form Write = + in standard form using integers. = + = Q R Multipl each side b. = + Use the Distributive Propert. - + = Subtract from each side. The standard form of = + is - + =. Write = + in standard form using integers. ± You can write equations for real-world situations using standard form. JETIVE Teaching Notes Real-World Problem Solving 00 Teaching Tip Show students how the equation in standard form could also be - =-. Encourage skeptical students to rewrite this equation in -intercept form and compare it to the equation given in the eample. Diversit Some students ma not be familiar with swimming laps. sk a student who is eperienced in swimming laps to describe the activit. sk the student to estimate the average amount of time it would take a person to swim a lap in a pool. dditional Eamples Write = + in standard form using integers. ± or Using the table below, write an equation in standard form to find the number of hours ou would need to work at mowing lawns and delivering newspapers to make a total of $0. ± 0 mount paid Job per hour Mowing lawns $ Delivering newspapers $ heck Understanding 00 hapter Linear Equations and Their Graphs losure sk: How do ou find the - and -intercepts of a linear equation? To find the -intercept, substitute 0 for, then solve for. To find the -intercept, substitute 0 for, Data nalsis Write an equation in standard form to find the minutes someone who weighs 0 lb would need to biccle and swim laps in order to burn 00 calories. Use the data below. Define Let iccling Let ctivit b a 0-lb Person alories urned per Minute = the minutes spent biccling. = the minutes spent swimming laps. 0? minutes? minutes Relate plus equals biccling swimming laps Write 0 + = The equation in standard form is 0 + = owling Hiking 7 Running. mi/h Swimming, laps Walking. mi/h 00 calories Data nalsis Write an equation in standard form to find the minutes someone who weighs 0 lb would need to bowl and walk to burn 0 calories. ± 0 then solve for. Write = - in standard form. ± 00 pages 0 0. Eercises

4 EXERISES Practice and Problem Solving Practice b Eample Eample (page 99) Eample (page 99) Eample (page 99) Eample (page 00) Eample (page 00) a. nswers ma var. Sample: no. of cars; no. of vans or trucks 7a. nswers ma var. Sample: time walking; time running Find the - and -intercepts of each equation.. + = ; 9. - = 9 ; = 0 ; =-9 9 ;. + =- ;. 9 - =-7 ; =- ;. 7 - = 7 ; = 0 ; Match each equation with its graph = = 0. + = 0... For more practice, see Etra Practice. Graph each equation using - and -intercepts.. See margin.. + =. + =-. - = = =-. - = For each equation, tell whether its graph is a horizontal or a vertical line. 9. =- 0. =. =. =-.7 horizontal vertical horizontal vertical Graph each equation.. See back of book.. =. =-7. =-.. =. Write each equation in standard form using integers. 7. = + ±. = = - 0. = +. = -. = - 7 ±. = 7 +. = + 0. =- ± ± 0 ± 0. Fund-Raising The sophomore class holds a car wash to raise mone. local merchant donates all of the supplies. wash costs $ per car and $.0 per van or truck. a. Define a variable for the number of cars. Define a different variable for the number of vans or trucks. See left. b. Write an equation in standard form to relate the number of cars and vans or trucks the students must wash to raise $00. ± Fitness Larr runs at an average rate of mi/h. He walks at an average rate of mi/h. a. Define a variable for time spent walking. Define a different variable for time spent running. See left. b. Write an equation in standard form to relate the times he could spend running and walking if he travels a distance of mi. ±. Practice ssignment Guide bjective ore,, 9 7 Etension, bjective ore 7 7, 7,, Etension Standardized Test Prep 9 Mied Review 70 7 Technolog Tip Eercise 9 Suggest that studets press so the tick marks will be evenl spaced and the figure is not distorted. Enrichment - Reteaching - Practice - Pearson Education, Inc. ll rights reserved. Name lass Date Practice - Graph each equation using - and -intercepts. Standard Form. + =. + = =. - =-0. + =. 7 + = 7. =-.. - = 9. = 0. - =-. + = =. + =. - + =. + =. - = 7. - =. + = 9. =-. 0. = Write each equation in standard form using integers.. = -. = -. =- -. = -.. = =- -. The drama club sells 00 lb of fruit to raise mone. The fruit is sold in -lb bags and 0-lb bags. a. Write an equation to find the number of each tpe of bag that the club should sell. b. Graph our equation. c. Use our graph to find two different combinations of tpes of bags.. The student council is sponsoring a carnival to raise mone. Tickets cost $ for adults and $ for students. The student council wants to raise $0. a. Write an equation to find the number of each tpe of ticket the should sell. b. Graph our equation. c. Use our graph to find two different combinations of tickets sold.. nna goes to a store to bu $70 worth of flour and sugar for her baker. bag of flour costs $, and a bag of sugar costs $7. a. Write an equation to find the number of bags of each tpe nna can bu. b. Graph our equation.. You have $0 to spend on cold cuts for a part. Ham costs $.99/lb, and turke costs $.99/lb. Write an equation in standard form to relate the number of pounds of each kind of meat ou could bu. lgebra hapter Lesson - Practice Lesson - Standard Form

5 _ete0_0_9-0 /9/0 : PM Page 0. ssess ppl Your Skills Graph each equation.. See margin = = 0. - = Lesson Quiz - Find the - and -intercepts of each equation.. + =, = 9,. Graph - = using - and -intercepts.. - =-. = +. = = = -. = See back of book. 7. Nutrition Suppose ou are preparing a snack mi. You want the total protein from peanuts and granola to equal grams. Peanuts have 7 grams of protein per ounce, and granola has grams of protein per ounce. a. Write an equation for the protein content of our mi. ± 7 b. Graph our equation. Use our graph to find how man ounces of granola ou should use if ou use ounce of peanuts. See back of book.. You are sent to the store to bu sliced meat for a part. You are told to get roast beef and turke, and ou are given $0. Roast beef is $.9/lb and turke is $.99/lb. Write an equation in standard form to relate the pounds of each kind of meat ou could bu at the store with $0..9 ±.99 0 Graphing alculator Write each equation in slope-intercept form. Then use a graphing calculator to graph each equation. Make a sketch of the graph. Include the - and -intercepts. 9. See back of book. For each equation, tell whether its graph is horizontal or vertical.. = horizontal. =- vertical. Write = - in standard form using integers. ± or = =. + = =. + = =. Writing Two of the forms of a linear equation are slope-intercept form and standard form. Eplain when each is the more useful. See margin.. ritical Thinking The definition of standard form states that and can t both be zero. Eplain wh. 7. Error nalsis student sas that the equation + = is a standard form of the equation = +. What is the student s error? lternative ssessment rganize students into groups of four. Instruct each student to write an equation in slopeintercept form on a piece of paper, and then pass the paper to the student to the right. The net student rewrites the equation in standard form, then passes the paper to the right again. Now each student finds the - and -intercepts of the equation and passes the paper to the right again. Students graph the equations using the intercepts. Some intercepts ma be approimations. If the intercepts coincide at the origin, the need to find an additional point. Standardized Test Prep Resources For additional practice with a variet of test item formats: Standardized Test Prep, p. Test-Taking Strategies, p. 0 Test-Taking Strategies with Transparencies 0 hallenge c. nswers ma var. Sample: The - and - intercepts of ± are three times those of ±. 0 hapter Linear Equations and Their Graphs pages 0 0. Eercises Write an equation for each line on the graph. a. a 9. b 0. c. d. a. Fund-Raising Suppose our school is having a talent b show to raise mone for new music supplies. You estimate that 00 students and 0 adults will attend. You estimate $00 in epenses. Write an equation to d c find what ticket prices ou should set to raise $ s ± 0a 00 b. pen-ended Graph our equation. hoose three possible prices ou could set for students and adults tickets. Which is the best choice? Eplain.. Write an equation of a line that has the same slope as the line - = 7 and the same -intercept as the line - 9 =. ±. Geometr Graph each of the four lines below on the same graph. What figure do the four lines form? See left above. - + = 0 + =- - + =- + =. a. Graph + = and + =. See margin. b. What is the slope of each line? ; c. ompare the -intercepts of the two lines. How are the related? How are the -intercepts related? See left

6 Standardized Standardized Test ptest Prep Multiple hoice Short Response. [] ± ; [] correct slopeintercept equation Etended Response Take It to the NET nline lesson quiz at Web ode: aea-00 Mied Review Lesson - Lesson - Lesson -. Which of the following is the standard form of = + written using integers?. + =. - = -. + = D. - - = 7. Which is the slope of + =? H F. G. H. I.. basket with apples weighs pounds. The same basket with apples weighs pounds. Write an equation in slope-intercept form for the weight in terms of the number of apples. Write an equation in standard form with integer coefficients that shows the relationship of the weight and the number of apples. See left. 9. tire dealer sells Supreme tires for $ each and Prestige tires for $ each. During one week, the sales for both tires totaled $00. a. Write an equation that ou can use to determine the possible combinations of Supreme tires and Prestige tires sold. b. Graph our equation on a coordinate plane. c. Use our graph to list possible combinations of Supreme and Prestige tires sold. a c. See back of book. Determine whether the ordered pair is a solution of the equation. 70. (, -); = (, -); = - 7. (-, -7); =- - es no no Find each probabilit for rolling a number cube. 7. P(rolling a, then a ) 7. P(rolling a, then an even number) Solve each proportion. 7. a = 7. w = = = m m 9 heckpoint heckpoint Quiz Quiz Lessons - through - Instant self-check quiz online and on D-RM Find the slope of the line passing through each pair of points.. (-, ), (, -) 7. (, ), (0, ). (-, -), (-, -7). (, -), (-, ) hapter heckpoint To check understanding of Lessons - to -: heckpoint Quiz (p. 0) Teaching Resources heckpoint Quiz (also in Prentice Hall ssessment Sstem) Reaching ll Students Reading and Math Literac Spanish versions available. nswers ma var. Sample: slope-intercept form when comparing the steepness of two lines; standard form when making quick graphs a. page 0 heckpoint Quiz.. redit ards In 990, people charged $ billion on the two most-used tpes of credit cards. In 99, people charged $.0 trillion on these same two tpes of credit cards. What was the rate of change? $.7 billion per ear Graph each equation. 9. See margin.. = - 7. = +. + = = 0. Writing How are the graphs of = +, = +, and = + alike? How are the different? same -intercepts; different slopes 7.. Lesson - Standard Form