How can you write an equation of a line when you are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines
|
|
- Domenic Montgomery
- 6 years ago
- Views:
Transcription
1 .7 Writing Equations in Point-Slope Form How can ou write an equation of a line when ou are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines Work with a partner. Sketch the line that has the given slope and passes through the given point. Find the -intercept of the line. Write an equation of the line. a. m = b. m = Writing Equations In this lesson, ou will write equations of lines using a slope and a point. write equations of lines using two points. c. m = 7 d. m = 7 8 Chapter Graphing and Writing Linear Equations
2 ACTIVITY: Deriving an Equation Math Practice Construct Arguments How does a graph help ou derive an equation? Work with a partner. a. Draw a nonvertical line that passes through the point (,. b. Plot another point on our line. Label this point as (,. This point represents an other point on O the line. c. Label the rise and the run of the line through the points (, and (,. d. The rise can be written as. The run can be written as. Eplain wh this is true. e. Write an equation for the slope m of the line using the epressions from part (d. f. Multipl each side of the equation b the epression in the denominator. Write our result. What does this result represent? (, ACTIVITY: Writing an Equation Work with a partner. For months, ou saved $ a month. You now have $7 in our savings account. Draw a graph that shows the balance in our account after t months. Use our result from Activit to write an equation that represents the balance A after t months. Balance (dollars Savings Account A t Time (months. Redo Activit using the equation ou found in Activit. Compare the results. What do ou notice?. Wh do ou think = m( is called the point-slope form of the equation of a line? Wh do ou think it is important?. IN YOUR OWN WORDS How can ou write an equation of a line when ou are given the slope and a point on the line? Give an eample that is different from those in Activit. Use what ou learned about writing equations using a slope and a point to complete Eercises on page 88. Section.7 Writing Equations in Point-Slope Form 8
3 .7 Lesson Lesson Tutorials Ke Vocabular point-slope form, p. 8 Point-Slope Form Words A linear equation written in the form = m( is in point-slope form. The line passes through the point (,, and the slope of the line is m. slope (, Algebra = m( (, passes through (, O EXAMPLE Writing an Equation Using a Slope and a Point Write in point-slope form an equation of the line that passes through the point (, with slope. = m( Write the point-slope form. = [ ( ] Substitute for m, for, and for. = ( + Simplif. So, the equation is = ( +. Check Check that (, is a solution of the equation. = ( + Write the equation. =? ( + Substitute. 0 = 0 Simplif. Eercises Write in point-slope form an equation of the line that passes through the given point and has the given slope.. (, ; m =. (7, 0; m =. ( 8, ; m = 8 Chapter Graphing and Writing Linear Equations
4 Stud Tip EXAMPLE You can use either of the given points to write the equation of the line. Use m = and (,. ( = ( + = + 0 = + 8 Writing an Equation Using Two Points Write in slope-intercept form an equation of the line that passes through the points (, and (,. Find the slope: m = = = = Then use the slope m = and the point (, to write an equation of the line. = m( Write the point-slope form. = ( Substitute for m, for, and for. = + = + 8 Distributive Propert Write in slope-intercept form. EXAMPLE Real-Life Application You finish parasailing and are being pulled back to the boat. After seconds, ou are feet above the boat. (a Write and graph an equation that represents our height (in feet above the boat after seconds. (b At what height were ou parasailing? a. You are being pulled down at the rate of 0 feet per second. So, the slope is 0. You are feet above the boat after seconds. So, the line passes through (,. Use the point-slope form. = 0( Substitute for m,, and. 0 feet per second = = 0 + Distributive Propert Write in slope-intercept form. So, the equation is = 0 +. b. You start descending when = 0. The -intercept is. So, ou were parasailing at a height of feet (, 7 Eercises 7 Write in slope-intercept form an equation of the line that passes through the given points.. (,, (,. (,, (,. ( 8,, (, 9 7. WHAT IF? In Eample, ou are feet above the boat after seconds. Write and graph an equation that represents our height (in feet above the boat after seconds. Section.7 Writing Equations in Point-Slope Form 87
5 .7 Eercises Help with Homework. VOCABULARY From the equation = ( +, identif the slope and a point on the line.. WRITING Describe how to write an equation of a line using (a its slope and a point on the line and (b two points on the line. 9+(-= +(-= +(-9= 9+(-= Use the point-slope form to write an equation of the line with the given slope that passes through the given point.. m =. m =. m = Write in point-slope form an equation of the line that passes through the given point and has the given slope.. (, 0; m = 7. (, 8; m = 8. (, ; m = 9. (7, ; m = 7 0. (, ; m =. (, ; m = Write in slope-intercept form an equation of the line that passes through the given points.. (,, (,. (,, (,. (,, (, 7. (,, (8,. ( 9,, (, 7. (,, (, 8. CHEMISTRY At 0 C, the volume of a gas is liters. For each degree the temperature T (in degrees Celsius increases, the volume V (in liters of the gas increases b. Write an equation that represents the volume of the gas in terms of the temperature. 88 Chapter Graphing and Writing Linear Equations
6 9. CARS After it is purchased, the value of a new car decreases $000 each ear. After ears, the car is worth $8,000. a. Write an equation that represents the value V (in dollars of the car ears after it is purchased. b. What was the original value of the car? 0. REASONING Write an equation of a line that passes through the point (8, that is (a parallel and (b perpendicular to the graph of the equation =.. CRICKETS According to Dolbear s law, ou can predict the temperature T (in degrees Fahrenheit b counting the number of chirps made b a snow tree cricket in minute. For each rise in temperature of 0. F, the cricket makes an additional chirp each minute. a. A cricket chirps 0 times in minute when the temperature is 0 F. Write an equation that represents the temperature in terms of the number of chirps in minute. b. You count 00 chirps in minute. What is the temperature? c. The temperature is 9 F. How man chirps would ou epect the cricket to make? Leaning Tower of Pisa (0.7,. WATERING CAN You water the plants in our classroom at a constant rate. After seconds, our watering can contains 8 ounces of water. Fifteen seconds later, the can contains 8 ounces of water. a. Write an equation that represents the amount (in ounces of water in the can after seconds. b. How much water was in the can when ou started watering the plants? c. When is the watering can empt? 7.7 m. Problem Solving The Leaning Tower of Pisa in Ital was built between 7 and 0. a. Write an equation for the ellow line. b. The tower is meters tall. How far off center is the top of the tower? Graph the linear equation. (Section.. =. = +. = 7. MULTIPLE CHOICE What is the -intercept of the equation + = 0? (Section. A 0 B C D 0 Section.7 Writing Equations in Point-Slope Form 89
Graphing and Writing Linear Equations
Graphing and Writing Linear Equations. Graphing Linear Equations. Slope of a Line. Graphing Linear Equations in Slope-Intercept Form. Graphing Linear Equations in Standard Form. Writing Equations in Slope-Intercept
More informationComparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern
5.5 Comparing Linear and Nonlinear Functions in real life is linear or nonlinear? How can ou recognize when a pattern ACTIVITY: Finding Patterns for Similar Figures Work with a partner. Cop and complete
More informationSolving Polynomial Equations Exponential Growth in Factored Form
7.5 Solving Polnomial Equations Eponential Growth in Factored Form is written in factored form? How can ou solve a polnomial equation that Two polnomial equations are equivalent when the have the same
More informationACTIVITY: Comparing Types of Decay
6.6 Eponential Deca eponential deca? What are the characteristics of 1 ACTIVITY: Comparing Tpes of Deca Work with a partner. Describe the pattern of deca for each sequence and graph. Which of the patterns
More informationName Date. and y = 5.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationSystems of Linear Inequalities
. Sstems of Linear Inequalities sstem of linear inequalities? How can ou sketch the graph of a ACTIVITY: Graphing Linear Inequalities Work with a partner. Match the linear inequalit with its graph. + Inequalit
More informationSolving Systems of Linear Equations by Graphing
. Solving Sstems of Linear Equations b Graphing How can ou solve a sstem of linear equations? ACTIVITY: Writing a Sstem of Linear Equations Work with a partner. Your famil starts a bed-and-breakfast. The
More informationACTIVITY: Using a Table to Plot Points
.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
More informationComparing Linear, Exponential, and Quadratic Functions
. Comparing Linear, Eponential, and Quadratic Functions How can ou compare the growth rates of linear, eponential, and quadratic functions? ACTIVITY: Comparing Speeds Work with a partner. Three cars start
More informationHow can you construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot
9. Scatter Plots How can ou construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot Work with a partner. The weights (in ounces) and circumferences C (in inches) of several sports
More informationSimplifying Rational Expressions
.3 Simplifying Rational Epressions What are the ecluded values of a rational epression? How can you simplify a rational epression? ACTIVITY: Simplifying a Rational Epression Work with a partner. Sample:
More information( 3x. Chapter Review. Review Key Vocabulary. Review Examples and Exercises 6.1 Properties of Square Roots (pp )
6 Chapter Review Review Ke Vocabular closed, p. 266 nth root, p. 278 eponential function, p. 286 eponential growth, p. 296 eponential growth function, p. 296 compound interest, p. 297 Vocabular Help eponential
More informationEssential Question How can you solve a system of linear equations? $15 per night. Cost, C (in dollars) $75 per Number of. Revenue, R (in dollars)
5.1 Solving Sstems of Linear Equations b Graphing Essential Question How can ou solve a sstem of linear equations? Writing a Sstem of Linear Equations Work with a partner. Your famil opens a bed-and-breakfast.
More information) approaches e
COMMON CORE Learning Standards HSF-IF.C.7e HSF-LE.B.5. USING TOOLS STRATEGICALLY To be proficient in math, ou need to use technological tools to eplore and deepen our understanding of concepts. The Natural
More informationMaintaining Mathematical Proficiency
Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on
More informationUsing Intercept Form
8.5 Using Intercept Form Essential Question What are some of the characteristics of the graph of f () = a( p)( q)? Using Zeros to Write Functions Work with a partner. Each graph represents a function of
More informationc. Find the slope and y-intercept of the graph of the linear equation. Then sketch its graph.
Name Solve. End-of-Course. 7 =. 5 c =. One cell phone plan charges $0 per month plus $0.5 per minute used. A second cell phone plan charges $5 per month plus $0.0 per minute used. Write and solve an equation
More informationDiscrete and Continuous Domains
. Discrete and Continuous Domains How can ou decide whether the domain of a function is discrete or continuous? EXAMPLE: Discrete and Continuous Domains In Activities and in Section., ou studied two real-life
More informationFunctions. Essential Question What is a function?
3. Functions COMMON CORE Learning Standard HSF-IF.A. Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs
More informationFunctions. Essential Question What is a function? Work with a partner. Functions can be described in many ways.
. Functions Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs and the -coordinates are outputs. A relation
More informationFair Game Review. Chapter 9. Find the square root(s) ± Find the side length of the square. 7. Simplify Simplify 63.
Name Date Chapter 9 Find the square root(s). Fair Game Review... 9. ±. Find the side length of the square.. s. s s Area = 9 ft s Area = 0. m 7. Simplif 0. 8. Simplif. 9. Simplif 08. 0. Simplif 88. Copright
More informationWriting Equations in Point-Slope Form
. Writing Equations in Point-Slope Form Essential Question How can ou write an equation of a line when ou are given the slope and a point on the line? Writing Equations of Lines Work with a partner. Sketch
More informationLinear Functions. Essential Question How can you determine whether a function is linear or nonlinear?
. Linear Functions Essential Question How can ou determine whether a function is linear or nonlinear? Finding Patterns for Similar Figures Work with a partner. Cop and complete each table for the sequence
More informationReady To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities
A Read To Go n? Skills Intervention -1 Solving Linear Equations and Inequalities Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular equation solution of an equation linear
More informationFair Game Review. Chapter 8. Graph the linear equation. Big Ideas Math Algebra Record and Practice Journal
Name Date Chapter Graph the linear equation. Fair Game Review. =. = +. =. =. = +. = + Copright Big Ideas Learning, LLC Big Ideas Math Algebra Name Date Chapter Fair Game Review (continued) Evaluate the
More informationSolving Quadratic Equations by Graphing 9.1. ACTIVITY: Solving a Quadratic Equation by Graphing. How can you use a graph to solve a quadratic
9. Solving Quadratic Equations b Graphing equation in one variable? How can ou use a graph to solve a quadratic Earlier in the book, ou learned that the -intercept of the graph of = a + b variables is
More information9-3 Linear Functions Going Deeper
Name Class Date 9-3 Linear Functions Going Deeper Essential question: How do ou graph a linear function? 1 CC.8.EE.5 EXPLORE Investigating Change video tutor The U.S. Department of Agriculture defines
More informationHow can you determine the number of solutions of a quadratic equation of the form ax 2 + c = 0? ACTIVITY: The Number of Solutions of ax 2 + c = 0
9. Solving Quadratic Equations Using Square Roots How can ou determine the number of solutions of a quadratic equation of the form a + c = 0? ACTIVITY: The Number of Solutions of a + c = 0 Work with a
More information4 B. 4 D. 4 F. 3. How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?
3.1 Solving Quadratic Equations COMMON CORE Learning Standards HSA-SSE.A. HSA-REI.B.b HSF-IF.C.8a Essential Question Essential Question How can ou use the graph of a quadratic equation to determine the
More information1Write and graph. 2Solve problems. Now. Then. Why? New Vocabulary
Direct Variation Then You found rates of change of linear functions. (Lesson -) Now Write and graph direct variation equations. Solve problems involving direct variation. Wh? Bianca is saving her mone
More informationFair Game Review. Chapter = How many calculators are sold when the profit is $425? Solve the equation. Check your solution.
Name Date Chapter 4 Fair Game Review Solve the equation. Check our solution.. 8 3 = 3 2. 4a + a = 2 3. 9 = 4( 3k 4) 7k 4. ( m) 2 5 6 2 = 8 5. 5 t + 8t = 3 6. 3 5h 2 h + 4 = 0 2 7. The profit P (in dollars)
More informationCharacteristics of Quadratic Functions
. Characteristics of Quadratic Functions Essential Question What tpe of smmetr does the graph of f() = a( h) + k have and how can ou describe this smmetr? Parabolas and Smmetr Work with a partner. a. Complete
More informationFactoring Polynomials
5. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS 2A.7.D 2A.7.E Factoring Polnomials Essential Question How can ou factor a polnomial? Factoring Polnomials Work with a partner. Match each polnomial equation with
More informationChapter 4 ( 2, 2 ). Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 141) = = = = 15. The solution checks.
Chapter Chapter Opener Tr It Yourself (p. ). ab = ( ) = ( ) = = = =. a b = ( ). a b = = = = + = + = + 9 =, or. a ( b a ). Point Q is on the -ais, units up from the origin. So, the -coordinate is, and the
More informationf(x) = 2x 2 + 2x - 4
4-1 Graphing Quadratic Functions What You ll Learn Scan the tet under the Now heading. List two things ou will learn about in the lesson. 1. Active Vocabular 2. New Vocabular Label each bo with the terms
More informationInverse of a Function
. Inverse o a Function Essential Question How can ou sketch the graph o the inverse o a unction? Graphing Functions and Their Inverses CONSTRUCTING VIABLE ARGUMENTS To be proicient in math, ou need to
More informationGraphing Linear Functions The collection of all input values is called the of a function.
Math /7 NTES (9.3) Name Graphing Linear Functions The collection of all input values is called the of a function. The collection of all output values is called the of a function. Make a table for the function.
More informationEssential Question How can you determine whether a polynomial equation has imaginary solutions? 2 B. 4 D. 4 F.
5. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS 2A.7.A The Fundamental Theorem of Algebra Essential Question How can ou determine whether a polnomial equation has imaginar solutions? Cubic Equations and Imaginar
More informationEssential Question What is the equation of a circle with center (h, k) and radius r in the coordinate plane?
10.7 Circles in the Coordinate Plane Essential Question What is the equation of a circle with center (h, k) and radius r in the coordinate plane? The Equation of a Circle with Center at the Origin Work
More information1.1. Use a Problem Solving Plan. Read a problem and make a plan. Goal p Use a problem solving plan to solve problems. VOCABULARY. Formula.
. Georgia Performance Standard(s) MMPd, MMPa Your Notes Use a Problem Solving Plan Goal p Use a problem solving plan to solve problems. VOCABULARY Formula A PROBLEM SOLVING PLAN Step Read the problem carefull.
More informationSlope as a Rate of Change
Find the slope of a line using two of its points. Interpret slope as a rate of change in real-life situations. FINDING THE SLOPE OF A LINE The slope m of the nonvertical line passing through the points
More informationCan a system of linear equations have no solution? Can a system of linear equations have many solutions?
5. Solving Special Sstems of Linear Equations Can a sstem of linear equations have no solution? Can a sstem of linear equations have man solutions? ACTIVITY: Writing a Sstem of Linear Equations Work with
More informationEssential Question How can you solve a nonlinear system of equations?
.5 Solving Nonlinear Sstems Essential Question Essential Question How can ou solve a nonlinear sstem of equations? Solving Nonlinear Sstems of Equations Work with a partner. Match each sstem with its graph.
More informationEssential Question How can you use a scatter plot and a line of fit to make conclusions about data?
. Scatter Plots and Lines of Fit Essential Question How can ou use a scatter plot and a line of fit to make conclusions about data? A scatter plot is a graph that shows the relationship between two data
More informationWords Algebra Graph. 5 rise } run. } x2 2 x 1. m 5 y 2 2 y 1. slope. Find slope in real life
TEKS 2.2 a.1, a.4, a.5 Find Slope and Rate of Change Before You graphed linear functions. Now You will find slopes of lines and rates of change. Wh? So ou can model growth rates, as in E. 46. Ke Vocabular
More informationLESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II
LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS
More information7.5 Solve Special Types of
75 Solve Special Tpes of Linear Sstems Goal p Identif the number of of a linear sstem Your Notes VOCABULARY Inconsistent sstem Consistent dependent sstem Eample A linear sstem with no Show that the linear
More informationFunctions. Essential Question What are some of the characteristics of the graph of an exponential function? ) x e. f (x) = ( 1 3 ) x f.
7. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A Eponential Growth and Deca Functions Essential Question What are some of the characteristics of the graph of an eponential function? You can use a graphing
More informationREVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES
Etra Eample. Graph.. 6. 7. (, ) (, ) REVIEW KEY VOCABULARY quadratic function, p. 6 standard form of a quadratic function, p. 6 parabola, p. 6 verte, p. 6 ais of smmetr, p. 6 minimum, maimum value, p.
More informationModeling with Exponential and Logarithmic Functions 6.7. Essential Question How can you recognize polynomial, exponential, and logarithmic models?
.7 Modeling with Eponential and Logarithmic Functions Essential Question How can ou recognize polnomial, eponential, and logarithmic models? Recognizing Different Tpes of Models Work with a partner. Match
More information3.1 Graph Quadratic Functions
3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your
More informationLESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II
LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS
More informationChapter Review. Review Key Vocabulary. Review Examples and Exercises. 4.1 Graphing Linear Equations (pp ) Graph y = 3x 1.
Chapter Review Review Ke Vocabular linear equation p. solution of a linear equation, p., p. 0 rise, p. 0 run, p. 0 Vocabular Help x-intercept, p. 8 -intercept, p. 8 -intercept form, p. 8 standard form,
More informationP.4 Lines in the Plane
28 CHAPTER P Prerequisites P.4 Lines in the Plane What ou ll learn about Slope of a Line Point-Slope Form Equation of a Line Slope-Intercept Form Equation of a Line Graphing Linear Equations in Two Variables
More informationdecreases as x increases.
Chapter Review FREQUENTLY ASKED Questions Q: How can ou identif an eponential function from its equation? its graph? a table of values? A: The eponential function has the form f () 5 b, where the variable
More information4.6 Model Direct Variation
4.6 Model Direct Variation Goal p Write and graph direct variation equations. Your Notes VOCABULARY Direct variation Constant of variation Eample Identif direct variation equations Tell whether the equation
More informationMaintaining Mathematical Proficiency
Name Date Chapter 8 Maintaining Mathematical Proficienc Graph the linear equation. 1. = 5. = + 3 3. 1 = + 3. = + Evaluate the epression when =. 5. + 8. + 3 7. 3 8. 5 + 8 9. 8 10. 5 + 3 11. + + 1. 3 + +
More informationDomain, Range, and End Behavior
Locker LESSON 1.1 Domain, Range, and End Behavior Common Core Math Standards The student is epected to: F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship
More informationEVALUATING POLYNOMIAL FUNCTIONS
Page 1 of 8 6.2 Evaluating and Graphing Polnomial Functions What ou should learn GOAL 1 Evaluate a polnomial function. GOAL 2 Graph a polnomial function, as applied in Eample 5. Wh ou should learn it To
More informationNAME DATE PERIOD. Study Guide and Intervention. Ax + By = C, where A 0, A and B are not both zero, and A, B, and C are integers with GCF of 1.
NAME DATE PERID 3-1 Stud Guide and Intervention Graphing Linear Equations Identif Linear Equations and Intercepts A linear equation is an equation that can be written in the form A + B = C. This is called
More informationProperties of the Graph of a Quadratic Function. has a vertex with an x-coordinate of 2 b } 2a
0.2 Graph 5 a 2 b c Before You graphed simple quadratic functions. Now You will graph general quadratic functions. Wh? So ou can investigate a cable s height, as in Eample 4. Ke Vocabular minimum value
More informationMath Departmental Exit Assessment Review (Student Version)
Math 03 - Departmental Eit Assessment Review (Student Version) Factor completel. (Factoring Review) ) 6-6 - 0 ) 3-343 3) 3 - + 8-40 4) - 36 ) + - 6 + 9 + 8 - + + Add or subtract as indicated. Simplif completel.
More informationDetermining Slope and y-intercept 8.4.C. Find the slope of the line using the points (0, 4) and (-3, 6).
? LESSON. Determining Slope and -intercept ESSENTIAL QUESTION Proportionalit 8..C Use data from a table or graph to determine the rate of change or slope and -intercept in mathematical and real-world problems.
More informationMaintaining Mathematical Proficiency
Name Date Chapter Maintaining Mathematical Proficienc Use the graph to answer the question. A H B F G E C D x 1. What ordered pair corresponds to point A?. What ordered pair corresponds to point H? 3.
More information3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
Section. Logarithmic Functions and Their Graphs 7. LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Ariel Skelle/Corbis What ou should learn Recognize and evaluate logarithmic functions with base a. Graph logarithmic
More informationYou studied exponential growth and decay functions.
TEKS 7. 2A.4.B, 2A..B, 2A..C, 2A..F Before Use Functions Involving e You studied eponential growth and deca functions. Now You will stud functions involving the natural base e. Wh? So ou can model visibilit
More informationObjectives To solve quadratic equations using the quadratic formula To find the number of solutions of a quadratic equation
9-6 The Quadratic Formula and the Discriminant Content Standards A.REI..a Use the method of completing the square to transform an quadratic equation in into an equation of the form ( p) 5 q... Derive the
More informationIn grade 10, you used trigonometry to find sides and angles in triangles. For a right triangle, sin v hy
The Inverse Function 3. Part 1: Defining the Inverse Function In grade 10, ou used trigonometr to find sides and angles in triangles. For a opposite right triangle, sin v h. You saw that on a calculator,
More informationMaintaining Mathematical Proficiency
Chapter Maintaining Mathematical Proficienc Find the -intercept of the graph of the linear equation. 1. = + 3. = 3 + 5 3. = 10 75. = ( 9) 5. 7( 10) = +. 5 + 15 = 0 Find the distance between the two points.
More information(0, 2) y = x 1 2. y = x (2, 2) y = 2x + 2
. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G..B G..C Equations of Parallel and Perpendicular Lines Essential Question How can ou write an equation of a line that is parallel or perpendicular to a given line
More informationEvaluate Logarithms and Graph Logarithmic Functions
TEKS 7.4 2A.4.C, 2A..A, 2A..B, 2A..C Before Now Evaluate Logarithms and Graph Logarithmic Functions You evaluated and graphed eponential functions. You will evaluate logarithms and graph logarithmic functions.
More informationOriginal site. translation. transformation. Decide whether the red figure is a translation of the blue figure. Compare a Figure and Its Image
Page of 8 3.7 Translations Goal Identif and use translations. Ke Words translation image transformation In 996, New York Cit s Empire Theater was slid 70 feet up 2nd Street to a new location. Original
More information4.2 Parabolas. Explore Deriving the Standard-Form Equation. Houghton Mifflin Harcourt Publishing Company. (x - p) 2 + y 2 = (x + p) 2
COMMON CORE. d Locker d LESSON Parabolas Common Core Math Standards The student is epected to: COMMON CORE A-CED.A. Create equations in two or more variables to represent relationships between quantities;
More informationLaurie s Notes. Overview of Section 3.5
Overview of Section.5 Introduction Sstems of linear equations were solved in Algebra using substitution, elimination, and graphing. These same techniques are applied to nonlinear sstems in this lesson.
More informationMaintaining Mathematical Proficiency
Name Date Chapter 5 Maintaining Mathematical Proficienc Graph the equation. 1. + =. = 3 3. 5 + = 10. 3 = 5. 3 = 6. 3 + = 1 Solve the inequalit. Graph the solution. 7. a 3 > 8. c 9. d 5 < 3 10. 8 3r 5 r
More informationWhat You ll Learn Identify direct variation. Use direct variation to solve problems.
AM_S_C_L_3.indd Page // 3: PM s-user /Volumes//GO/CORE_READING/TENNESSEE/ANCILLARY... Proportionalit and Linear Relationships Teach the Concept Lesson - Direct Variation Interactive Stud Guide See pages
More information5.3 Interpreting Rate of Change and Slope
Name Class Date 5.3 Interpreting Rate of Change and Slope Essential question: How can ou relate rate of change and slope in linear relationships? Resource Locker Eplore Determining Rates of Change For
More information7-1. Exploring Exponential Models. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary. 1. Cross out the expressions that are NOT powers.
7-1 Eploring Eponential Models Vocabular Review 1. Cross out the epressions that are NOT powers. 16 6a 1 7. Circle the eponents in the epressions below. 5 6 5a z Vocabular Builder eponential deca (noun)
More information1.7 Inverse Functions
71_0107.qd 1/7/0 10: AM Page 17 Section 1.7 Inverse Functions 17 1.7 Inverse Functions Inverse Functions Recall from Section 1. that a function can be represented b a set of ordered pairs. For instance,
More informationFair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationExponential and Logarithmic Functions
Eponential and Logarithmic Functions.1 Eponential Growth and Deca Functions. The Natural Base e.3 Logarithms and Logarithmic Functions. Transformations of Eponential and Logarithmic Functions.5 Properties
More informationUse Properties of Exponents
4. Georgia Performance Standard(s) MMAa Your Notes Use Properties of Eponents Goal p Simplif epressions involving powers. VOCABULARY Scientific notation PROPERTIES OF EXPONENTS Let a and b be real numbers
More informationInfinite Limits. Let f be the function given by. f x 3 x 2.
0_005.qd //0 :07 PM Page 8 SECTION.5 Infinite Limits 8, as Section.5, as + f() = f increases and decreases without bound as approaches. Figure.9 Infinite Limits Determine infinite its from the left and
More information5.3 Interpreting Rate of Change and Slope - NOTES
Name Class Date 5.3 Interpreting Rate of Change and Slope NOTES Essential question: How can ou relate rate of change and slope in linear relationships? Eplore A1.3.B calculate the rate of change of a linear
More information11.1 Inverses of Simple Quadratic and Cubic Functions
Locker LESSON 11.1 Inverses of Simple Quadratic and Cubic Functions Teas Math Standards The student is epected to: A..B Graph and write the inverse of a function using notation such as f (). Also A..A,
More informationMHF 4U Unit 1 Polynomial Functions Outline
MHF 4U Unit 1 Polnomial Functions Outline Da Lesson Title Specific Epectations 1 Average Rate of Change and Secants D1., 1.6, both D1.1A s - Instantaneous Rate of Change and Tangents D1.6, 1.4, 1.7, 1.5,
More informationEssential Question How can you use a quadratic function to model a real-life situation?
3. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A A..E A..A A..B A..C Modeling with Quadratic Functions Essential Question How can ou use a quadratic function to model a real-life situation? Work with a partner.
More informationDerivatives 2: The Derivative at a Point
Derivatives 2: The Derivative at a Point 69 Derivatives 2: The Derivative at a Point Model 1: Review of Velocit In the previous activit we eplored position functions (distance versus time) and learned
More informationTEST 150 points
Math 130 Spring 008 Name: TEST #1 @ 150 points Write neatly. Show all work. Write all responses on separate paper. Clearly label the exercises. 1. A piecewise-defined function is given. 1- x if x< f (
More information15.2 Graphing Logarithmic
_ - - - - - - Locker LESSON 5. Graphing Logarithmic Functions Teas Math Standards The student is epected to: A.5.A Determine the effects on the ke attributes on the graphs of f () = b and f () = log b
More informationName Class Date. Solving by Graphing and Algebraically
Name Class Date 16-4 Nonlinear Sstems Going Deeper Essential question: How can ou solve a sstem of equations when one equation is linear and the other is quadratic? To estimate the solution to a sstem
More informationSolving Multi-Step Inequalities
. Solving Multi-Step Inequalities How can ou use an inequalit to describe the area and perimeter of a composite figure? ACTIVITY: Areas and Perimeters of Composite Figures Wor with a partner. a. For what
More informationFair Game Review. Chapter 5. feet and the length is 2x feet. Find the. perimeter of the garden. 24x 5 3. Name Date. Simplify the expression. 6.
Name Date Chapter 5 Fair Game Review Simplif the expression. 1. 2x + 5 x 2. 4 + 2d 4d 3. 7 8 + 6 3 4. 5 + 4z 3 + 3z 5. 4( s + 2) + s 1 6. ( ) 24x 5 3 7. The width of a garden is ( 4x 1) perimeter of the
More informationFair Game Review. Chapter 10
Name Date Chapter 0 Evaluate the expression. Fair Game Review. 9 +. + 6. 8 +. 9 00. ( 9 ) 6. 6 ( + ) 7. 6 6 8. 9 6 x 9. The number of visits to a website can be modeled b = +, where is hundreds of visits
More informationSolving Special Systems of Linear Equations
.....5 Solving Sstems of Linear Equations Solving Sstems of Linear Equations b Graphing Solving Sstems of Linear Equations b Substitution Solving Sstems of Linear Equations b Elimination Solving Special
More informationFair Game Review. Chapter 5. Input, x Output, y. 1. Input, x Output, y. Describe the pattern of inputs x and outputs y.
Name Date Chapter Fair Game Review Describe the pattern of inputs and outputs.. Input, utput,. 8 Input, utput,. Input, 9. utput, 8 Input, utput, 9. The table shows the number of customers in hours. Describe
More information14.1 Systems of Linear Equations in Two Variables
86 Chapter 1 Sstems of Equations and Matrices 1.1 Sstems of Linear Equations in Two Variables Use the method of substitution to solve sstems of equations in two variables. Use the method of elimination
More information13.2 Exponential Growth Functions
Name Class Date. Eponential Growth Functions Essential Question: How is the graph of g () = a b - h + k where b > related to the graph of f () = b? A.5.A Determine the effects on the ke attributes on the
More information2.1 The Rectangular Coordinate System
. The Rectangular Coordinate Sstem In this section ou will learn to: plot points in a rectangular coordinate sstem understand basic functions of the graphing calculator graph equations b generating a table
More informationMini-Lecture 8.1 Solving Quadratic Equations by Completing the Square
Mini-Lecture 8.1 Solving Quadratic Equations b Completing the Square Learning Objectives: 1. Use the square root propert to solve quadratic equations.. Solve quadratic equations b completing the square.
More information