Simplify each expression (x - 5) 3x ± (x + 2) 5x ± New Vocabulary point-slope form. = m Use the definition of slope.

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1 -. Plan bjectives To graph and write linear equations using point-slope form To write a linear equation using data Eamples Graphing Using Point-Slope Form Writing an Equation in Point-Slope Form Using Two Points to Write an Equation Writing an Equation Using a Table Real-World Problem Solving - What You ll Learn To graph and write linear equations using point-slope form To write a linear equation using data... And Wh To write an equation relating altitude and the boiling point of water, as in Eample Point-Slope Form and Writing Linear Equations Check Skills You ll Need G for Help Lessons - and - Find the rate of change of the data in each table Simplif each epression.. -( - ) ±. ( + ) ± 0. ( ) New Vocabular point-slope form ± 7.. Math Background No matter what form a linear equation is written in, the coordinates of ever point on the graph of the line satisf its linear equation and, conversel, ever pair of values that satisf the equation represent a point on the graph. More Math Background: p. 0D Lesson Planning and Resources See p. 0E for a list of the resources that support this lesson. Part Using Point-Slope Form You can use the definition of slope to find another form of a linear equation called the point-slope form. = m Use the definition of slope. Suppose ou know that a line passes through the point (, ) and has slope. = Substitute (, ) for (, ) and substitute (, ) for (, ). Substitute for m. ( - ) = ( - ) Multipl each side b. - = ( - ) Simplif the left side of the equation. The equation - = ( - ) is in point-slope form. - = ( - ) Q c a -coordinate slope -coordinate Bell Ringer Practice Check Skills You ll Need For intervention, direct students to: Rate of Change and Slope Lesson -: Eample Etra Skills and Word Problem Practice, Ch. The Distributive Propert Lesson -: Eample Etra Skills and Word Problem Practice, Ch. Ke Concepts Definition Point-Slope Form of a Linear Equation Chapter Linear Equations and Their Graphs Special Needs L In Eample, to help an confusion about the signs, students graph a line and label two points. Then the write an equation for slope using the coordinates of the points. Ask: What operation do ou use to find the rise or the run? subtraction learning stle: verbal The point-slope form of the equation of a nonvertical line that passes through the point (, ) and has slope m is - = m( - ) Below Level L In Step of Eample, have students write equations in point-slope form using each ordered pair in the table. Then ask them to show that all four equations are equivalent. learning stle: verbal

2 . Graph the equation - = (, ) (, ) Graphing Using Point-Slope Form ( ). The equation shows that the line passes through (, ) and has a slope. Start at (, ). Using the slope, go up unit and right units to (, ). Draw a line through the two points. Graph the equation - = ( ). See left.. Teach Guided Instruction Additional Eamples Graph the equation - = ( - ). Vocabular Tip Square brackets, [ ], are grouping smbols commonl used when parentheses, ( ), are inside. For: Point-Slope Activit Use: Interactive Tetbook, - Writing an Equation in Point-Slope Form Write the equation of the line that has slope - that passes through the point (-, 7). - = m ( - ) Use the point-slope form. - 7 = -[ - (-)] Substitute (, 7) for (, ) and for m. - 7 =-( + ) Simplif inside the grouping smbols. Write the equation of the line that has slope that passes through the point (0, -). ( 0) If ou know two points on a line, first use them to find the slope. Then ou can write an equation using either point. Using Two Points to Write an Equation Write equations for the line in point-slope form and in slope-intercept form. (, ) Step Find the slope. = m = The slope is. (, ) Step Use either point to write the Step Rewrite the equation equation in point-slope form. from Step in slope- Use (, ). intercept form. - = m( - ) - = ( ) - = - = - ( ) = - a. Write an equation for the line in Eample in point-slope form using the point (-, -). ± ( ± ) b. Write the equation ou found in part (a) in slope-intercept form. c. What is true about the equation ou wrote in part (b) and the equation in Step of Eample? The are the same. Lesson - Point-Slope Form and Writing Linear Equations 7 Write the equation of the line with slope - that passes through the point (, -). ± ( ) Write equations for the line in point-slope form and in slopeintercept form. ( ± ) ± (, ) (, ) Advanced Learners L Have students write the slope-intercept form of the linear equation found in of Eample. Ask them what the -intercept in the equation represents. learning stle: verbal English Language Learners ELL Be sure that students understand that when a linear equation is written in Point-Slope form, the can identif a point on, and the slope of the graph of the equation just b looking at the equation. learning stle: verbal 7

3 Connection to Science Boiling point is defined as the temperature at which the vapor pressure of a liquid slightl eceeds the pressure of the atmosphere above the liquid. Water at atmosphere pressure boils at F. If the pressure on a liquid is reduced, the boiling point is lowered. Air pressure is less at higher elevations. Denver, Colorado is mile above sea level, so the boiling point of water there averages 0 F. Additional Eamples Is the relationship shown b the data linear? If so, model the data with an equation. es; ( ) Is the relationship shown b the data linear? If so, model the data with an equation. no Part Writing Linear Equations Using from Data You can write a linear equation to model data in tables. Two sets of data have a linear relationship if the rate of change between consecutive pairs of data is the same. For data that have a linear relationship, the rate of change is the slope. Writing an Equation Using a Table Is the relationship shown b the data linear? If so, model the data with an equation. Step Find the rate of change for Step Use the slope and a point consecutive ordered pairs. to write an equation. - = m ( - ) Is the relationship shown b the data at the right linear? If so, model the data with an equation. Yes; answers ma var. Sample: ( ) Real-World Problem Solving Substitute (, 7) for (, ) and for m. - 7 = ( ) Is the relationship shown b the data linear? If so, model the data with an equation Boiling Point of Water Altitude (000 ft).. Temperature (ºF) Resources Dail Notetaking Guide - L Dail Notetaking Guide - Adapted Instruction L Closure Ask students to write a set of data that is linear, and then model the data with an equation. Have them graph the data and the equation. Real-World Connection At 0 feet above sea level it takes 7 minutes to hard-boil an egg. This is more than 0% longer than it takes the same egg to cook at sea level. Step Find the rates of change for consecutive ordered pairs.. =-..7 = =-. The relationship is linear. The rate of change is -. degrees Fahrenheit per 000 ft of altitude. Step Use the slope and a point to write an equation. - = m ( - ) Use the point-slope form = -.( - ) Substitute (, 0.) for (, ) and. for m. The equation - 0. =-.( - ) relates altitude in thousands of feet to the boiling point temperature in degrees Fahrenheit. Chapter Linear Equations and Their Graphs pages Eercises 0. ± ( ). ( ). (). ± 7 ( ± ) 7. ± ( ). ( ± ); ±. ( ). ( ± ) 0.. ± ( ) 0. Answers ma var from ( ); the point indicated b. 0( ± ) or the equation.

4 G Is the relationship shown b the data in the table linear? If it is, model the data with an equation. Yes; answers ma var. Sample: 0 00 ( ) Temperature ºF ºF ºF Working utdoors Calories Burned per Da ºF 0 In Eample ou could rewrite - 0. =-.( - ) as =-. +. This form gives ou useful information about the -intercept. For instance, F is the boiling point of water at sea level. Here are the three forms of linear equations ou have studied. Ke Concepts Summar Linear Equations for Help For more help with the three forms of a linear equation, see page. Slope-Intercept Form Standard Form Point-Slope Form = m + b A + B = C ( - ) = m( - ) m is the slope and b Aand B are (, ) lies on the is the -intercept. not both 0. graph of the equation, and m is the slope. Eamples =- + + = - =- ( - ). Practice Assignment Guide A B -0, -, - A B -,,, 0 C Challenge - Test Prep - Mied Review 70- Homework To check students understanding of ke skills and concepts, go over Eercises,, 0,, 7. Error Prevention! Eercises 0 Suggest to students that the circle the -coordinates and bo the -coordinates. EXERCISES Practice and and Problem Solving A G Practice b Eample for Help Eample (page 7) Eample (page 7) Eample (page 7) For more eercises, see Etra Skill and Word Problem Practice. Graph each equation.. See back of book.. - = ( - ). - = ( - ). - = ( ). + =-( - ). + = ( ). - =-( + ) 7. + =-( - ). - = ( - ). - = ( + ) Write an equation in point-slope form for the line through the given point that has the given slope. 0. See margin. 0. (, -); m =. (, ); m =. (0, ); m =. (-, -7); m =. (, 0); m =. (, -); m =-. (-, ); m = 0 7. (, -); m =. (-, ); m = A line passes through the given points. Write an equation for the line in pointslope form. Then rewrite the equation in slope-intercept form. 0. See margin.. (-, 0), (, ) 0. (, ), (0, 0). (, -), (, -). (, -), (-, ). (-, -), (-7, -). (-, -), (, -). (, 7), (, -). (-, ), (, ) 7. (, -), (-, ). R, (, ). Q, R,, R 0. (0.,.), (7, ) Lesson - Point-Slope Form and Writing Linear Equations. ± ( );. ± ( ± );. 7 ( ); ±. ± ( );. ± ( ± );. 7( ± ); ± 7 ± 7 GPS Enrichment Guided Problem Solving Reteaching Adapted Practice Practice Name Class Date Practice - Point-Slope Form and Writing Linear Equations Write an equation in point-slope form for the line through the given points or through the given point with the given slope.. (, 7), (, ). (-, ); m =-. (, ), (, ). (-, ); m =. (, 7); m =. (, -); m = 7. (0, ), (-, ). (, ), (, ). (, ), (-, -) 0. (, ), (, 0). (0, -7); m =-. (-, ), (, ). (, ); m undefined. (-, 7); m =. (, -), (7, ). (7, ); m = 0 7. (, -), (, ). (, ), (, ). (-, ), (-0, ) 0. (, ); m =. (, -); m =-. (,.); m = 0.. (-, ); m =. (00, 0), (0, 0). (-, ), (, -). (, 7), (, ) 7. (, 7); m =. (-, ); m = Is the relationship shown b the data linear? If it is, model the data with an equation Write an equation of each line in point-slope form ± ( );. ( );. ( ); ± ( 0.);.. ± 7.. L L L L L Pearson Education, Inc. All rights reserved.

5 . Assess & Reteach Lesson Quiz. Graph the equation + =-( - ). Eample (page ). Yes; answers ma var. Sample: ( ± ). Yes; answers ma var. Sample: 0 ( ) Eample (page ). Yes; answers ma var. Sample: 7 0( 0) Is the relationship shown b the data linear? If so, model the data with an equation.. See left.. See left.. no no Speed ver Posted Fine See Volume Weight Speed (mi/h) ($) left. (gal) (lb) Write an equation of the line with slope - that passes through the point (0, ). ( 0), or +. Write an equation for the line that passes through (, -) and (-, ) in point-slope form and slope-intercept form. ± ( ); 7 =. Is the relationship shown b the data linear? If so, model that data with an equation. es; ± ( 0) B Appl Your Skills Write an equation of each line in point-slope form.. Answers ma var from point indicated b the equation ( ) ± ( ) 7 ( ) Write one equation of the line through the given points in point-slope form and one in standard form using integers.. See margin.. (, ), (-, ) 0. (, -), (-, -). (0, 0), (-, -). (0, ), (-, ). (-, ), (, ). (, ), (-, ). (, -), (, ). (, ), (-, 7) 7. (-7, ), (, -). (-, ), (-, -). (, ), (-, -) 0. (, ), (, ). (0, ), (-, 0). (-, ), (0, -). (, ), (, -) Alternative Assessment Let students work in pairs. Instruct each student to write coordinates for two points, and then write an equation passing through those points in pointslope form. Have each pair echange points and repeat. Then compare answers to check. P R E S S U R E I N C R E A S E S A scuba diver can descend to about feet. The submersible Alvin can descend to about. miles. In 0, the submersible Trieste descended to a record depth of. miles.. Science At the surface of the ocean, pressure is atmosphere. At ft below sea level, the pressure is atmospheres. The relationship of pressure and depth is linear. a. Write an equation for the data. ± b. Predict the pressure at 00 ft below sea level. about atmospheres. Environment Worldwide carbon monoide emissions are decreasing about. GPS million metric tons each ear. In, carbon monoide emissions were 7 million metric tons. Use a linear equation to model the relationship between carbon monoide emissions and time. Let = correspond to.. ±.. a. pen-ended Write an equation in point-slope form that contains the point (-, -). Eplain our steps. a b. See margin. b. How man equations could ou write in part(a)? Eplain. 7. Critical Thinking How would the graph of - = ( - ) change if all of the subtraction signs were changed to addition signs? -intercept changes from to.. Reasoning Is - = ( - ) an equation of a line through (, )? Eplain. Yes; the point satisfies the equation. 0 Chapter Linear Equations and Their Graphs pages 07 0 Eercises. ( ); ± 0. ± 0( ); 0. ± ( ± ); ± 0. 0( 0); 7. ( ± );. ± ( ); ± 7 ±. ( );. ( ); ± ±

6 G nline Homework Help Visit: PHSchool.com Web Code: ate-00 C Challenge 0. Answers ma var. Sample: a. ( 0) b. m/s c. m/s Standardized Test PrepTest Prep Gridded Response Mied Review. pen-ended Write an equation in each of the following forms. a. slope-intercept form ± a-c. Answers ma var. b. standard form ± Sample is given. c. point-slope form ( 0) 0. Science Use the scatter plot. See below a. Write an equation to model the data. left. b. What is the speed of sound at C? c. Predict the speed of sound at 0C. 0 Write an equation in slope-intercept form 0 of each line described below. 0. The line contains the point (-, -) and has the same slope as + = 7( + ). 7 ± Temperature ( C). The line contains the point (, ) and has the same -intercept as - = ( -).. The line contains the point (, -) and has the same -intercept as + = ( - ).. The table shows data that ou can model using a linear function. a. Find the value of when =..7 b. Find the value of when = c. Find the value of when =. d. Find the value of when = What is the slope of the graph of - = ( )?. Find the -intercept of the line + = ( + ). Effect of Air Temperature on Speed of Sound 7 7. What is the -intercept of the line = - 7?. When - = ( ) is written in standard form using positive integers, what is the smallest possible coefficient of?. When = + is written in standard form using positive integers, what is the smallest possible coefficient of? Speed (m/s). 7. Test Prep A sheet of blank grids is available with the Test-Taking Strategies with Transparencies booklet. Give this sheet to students for practice with filling in the grids. Resources For additional practice with a variet of test item formats: Standardized Test Prep, p. Test-Taking Strategies, p. Test-Taking Strategies with Transparencies a. Answers ma var. Sample: ± ( ± ); chose slope and substituted into m( ) b. Infinitel man; an real number can be used for the slope G for Help Lesson - Graph each line See margin = = = 7. - = 7. + = =- 7. Lesson -7 Find the common difference of each sequence. Then write the net two terms. 7. -, -7, -, c;, 77. 7,,, c ;, 7..,.,., c 0.07;., , -., -.,... 0.,,,...7;,. -7, -,,... ;, 0.0;.,. 7. lesson quiz, PHSchool.com, Web Code: ata-00 Lesson - Point-Slope Form and Writing Linear Equations 7. ( ± 7); ±. ( ± ); ±. ( ); ± 0 0. ( ); ±. ; ±. ( ± ); ± 0. ( ); ± 7.