Today I am: using scatterplots and lines of best fit to make predictions. So that I can: learn to write equations of lines of best fit.
|
|
- Rafe Palmer
- 5 years ago
- Views:
Transcription
1 LESSON 12 Lines of Best Fit LEARNING OBJECTIVES Toda I am: using scatterplots and lines of best fit to make predictions. So that I can: learn to write equations of lines of best fit. I ll know I have it when I can: write the equation of a line with two points. In Lesson 11, ou graphed and analzed a variet of scatterplots. In this lesson, ou ll further explore how to write the equation of a line to describe the scatterplot. Your equations will allow ou to make predictions about the data. Opening Exercise Reading Graphs 1. What data is this graph displaing? Tpheerafarge 2. Are ou surprised b this data? Explain. Yes for 12 ear olds s 0 Source: CrackSAT.net Who is Dann/Shutterstock.com 171
2 172 Module 1 Descriptive Statistics Exploration: Writing an Equation of a Line The equation of a line can be in the form = mx + b, where m represents the slope of the line and I b represents the -intercept. We ll start with a strong positive linear scatterplot. The line of best fit has been drawn in for ou. I Source: 3&filename IntroductorMathematics_DataAnalsisMethods.xml 3. Choose two points on the line of best fit and then determine the slope between these two lines. Y X z Y z O 6 2 Il A. M Points: ( ) and ( ) B. Slope using m two points: m 2 1 = x x C. What does this slope mean in terms of the data? The distance increasesb 2.5 m ever second m/sec 4. What is the estimated -intercept for the line? 6 5. Write the equation of the best fit line using mx b, where m slope and b -intercept. 2 5 X t 6
3 Unit 2 Scatterplots and Lines of Best Fit Lesson 12 Lines of Best Fit The slope of the line shown is 2.5. Did ou get that value? If not, how much did our slope differ from this value? Wh do ou think there might be a difference? Oh eah 7. The -intercept generated using the actual data points and a calculator or computer program 0 was 6. How much did our -intercept differ from this value? Wh do ou think there might be a difference? Oh eah 8. You can use our equation to find other points on the line. A. Use the graph to estimate the distance when time is 7.5 seconds. Y 2.5 G 5 16 X M B. Use our equation from Exercise 5 to estimate the distance when time is 7.5 seconds. C. Which model (graph or equation) would ou use to estimate the distance at 10 seconds? What is that value? Which model is more accurate? Equation is more accurate D. How much time would ou estimate would go b for 15 meters? Which model did ou use? Wh? O G G X 3.6 s Y
4 X 174 Module 1 Descriptive Statistics Practice Writing & Graphing Equations of Lines For Exercise 9 14, use the given information to write an equation of the line. Then graph the line. mxtb 9. Slope 3; -intercept 4 m b 10. Slope ½; -intercept Slope 1; -intercept ¼ 3X x 14 T 2 m 4 3T b i of i I 12. Two points on the line 13. Two points on the line (4, 4) and (8, 5) with a ( 3, 9) and (0, 5) with a -intercept of 3. -intercept of 5. Fx m I s 14. Two points on the line ( 2, 0) and (4, 6) with a -intercept of 2. X 2 I 14 b E
5 Unit 2 Scatterplots and Lines of Best Fit Lesson 12 Lines of Best Fit 175 Practice Writing Equations of Lines from Graphs For Exercise determine the slope and -intercept of the line. Then write the equation of the line g M O 0,2 3 F m 3z Slope Slope Slope -intercept -intercept -intercept 3 x th Slope -intercept Slope -intercept I 1 X 11 Slope -intercept
6 176 Module 1 Descriptive Statistics Point-Slope Form of a Line The equation ou wrote in Exercise 3 is in slope-intercept form or mx b. Point-slope is another ver useful form of a linear equation. For point-slope we need an point on the line and the slope. When no -intercept is available, we can use a different form of the equation of a line. This new form comes from the slope formula. 21. How did the get from the slope equation to the point-slope equation? 22. Suppose two points on the line in Exercise 3 are (1, 8.5) and (7, 23.5). A. Use the point-slope equation to write the equation of the line. Find the slope: Use the formula. You ma use either point for the equation: B. Discuss with our partner how ou could rearrange this equation to isolate the and get it in slope-intercept form. slope = m = 2 1 x x Gaga 2 1 or m = 2 1 x2 x1 2 1 ( 2 1) O Point-Slope Equation of a Line: = mx x or = mx x m Yz Y mcx2 x 92 Y TX i mcx m 23j5 5 lg5 25 2s5 ( ) 1 1 x.it CX sapoint m slope X l C. Rewrite our equation in Part A in slope-intercept form. 0 D. How does this equation compare to the one ou wrote in Exercise 5? point slope slope intercept X 1 ee
7 o Unit 2 Scatterplots and Lines of Best Fit Lesson 12 Lines of Best Fit What information do ou need to find the equation of a line? List all possibilities. If I have... Then I can use... Y slope m intercepts Y mxtb slopeandapoint or mcx x two points ix is apoint Practice Writing and Graphing Linear Equations For Exercise 24 26, write the equation of the line in point-slope form. Then graph the line. X Slope 3; Point ( 4, 7) 25. Slope ½; Point ( 5, 0) 26. Slope 1; Point ( ½, 4) t
8 178 Module 1 Descriptive Statistics Practice Writing and Graphing Linear Equations For Exercise write the slope and equation for the line. Then graph the line. 27. Point ( 1, 2); Point (3, 7) Slope: , Point ( 3, 5); Point (5, 0) Slope: 29. Point (8, 0); Point (4, 4) Slope: I E E Writing Equations of Lines Lesson Summar If ou have two points on our line, ou can use the Point-Slope Equation given b = mx x, where m slope and (x 1, 1 ) is a point on the line. ( ) 1 1 If ou have one point and the slope of our line, ou can use the Slope-Intercept Equation given b mx b, where m slope and b -intercept.
9 Unit 2 Scatterplots and Lines of Best Fit Lesson 12 Lines of Best Fit 179 NAME: PERIOD: DATE: Homework Problem Set 1. Graph the following lines. A. = 2 x 4 B. 3x Write the equation of the line in slope-intercept form. A. B.
10 180 Module 1 Descriptive Statistics 3. A. Wh is mx b called slope-intercept form and 1 = m( x x1) is called pointslope form? B. If ou wanted to change an equation from point-slope to slope-intercept form, what would ou do? 4. Change 3 2(x 1) to slope-intercept form. 5. Write the equation of the line in point-slope form. Then change the equation to slope-intercept form and graph the equation to see if our calculations were correct. A. (5, 1) and m 2 B. (2, 2) and (10, 2) Point-Slope: Slope-Intercept:
11 Unit 2 Scatterplots and Lines of Best Fit Lesson 12 Lines of Best Fit Write the equation in both point-slope and slope-intercept forms. A. (2, 5) and (5, 1) B. (0, 5) and m = 1 3 Point-slope form: Slope-intercept form: 7. Write the equation of the line represented b the data in the table. Write our answer in slopeintercept and point-slope forms. x Point-slope form: Slope-intercept form:
12 182 Module 1 Descriptive Statistics 8. Write the equation of the line in point-slope and slope-intercept forms. Point-slope form: Slope-intercept form: Spiral REVIEW Lines of Best Fit 9. Rachel misunderstood how a line of best fit works. Her line is shown below. What might have Rachel been considering when she drew this line? 10. Josh drew the line of best fit as shown below. Explain to Josh wh his line is not appropriate for this data.
Algebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form.
T328 [OBJECTIVE] The student will graph lines described by equations in standard form. [MATERIALS] Student pages S125 S133 Transparencies T336, T338, T340, T342, T344 Wall-size four-quadrant grid [ESSENTIAL
More informationName: Date: Period: Activity 4.6.2: Point-Slope Form of an Equation. 0, 4 and moving to another point on the line using the slope.
Name: Date: Period: Activity.6.2: Point-Slope Form of an Equation 1.) Graph the equation y x = + starting at ( ) 0, and moving to another point on the line using the slope. 2.) Now, draw another graph
More informationMathematics Success Grade 8
Mathematics Success Grade 8 T429 [OBJECTIVE] The student will solve systems of equations by graphing. [PREREQUISITE SKILLS] solving equations [MATERIALS] Student pages S207 S220 Rulers [ESSENTIAL QUESTIONS]
More information4-7 Point-Slope Form. Warm Up Lesson Presentation Lesson Quiz
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Find the slope of the line containing each pair of points. 1. (0, 2) and (3, 4) 2. ( 2, 8) and (4, 2) 1 3. (3, 3) and (12,
More informationLesson 12: Avi & Benita s Repair Shop
: Avi & Benita s Repair Shop Opening Exercise Avi and Benita run a repair shop. They need some help, so they hire you. Avi and Benita have different options for how much they'll pay you each day. In this
More informationAlgebra I Notes Unit Seven: Writing Linear Equations
Sllabus Objective.6 The student will be able to write the equation of a linear function given two points, a point and the slope, table of values, or a graphical representation. Slope-Intercept Form of
More informationt s time we revisit our friend, the equation of a line: y = mx + b
CH PARALLEL AND PERPENDICULAR LINES INTRODUCTION I t s time we revisit our friend, the equation of a line: mx + b SLOPE -INTERCEPT To be precise, b is not the -intercept; b is the -coordinate of the -intercept.
More informationSection 1.3. Slope formula: If the coordinates of two points on the line are known then we can use the slope formula to find the slope of the line.
MATH 11009: Linear Functions Section 1.3 Linear Function: A linear function is a function that can be written in the form f(x) = ax + b or y = ax + b where a and b are constants. The graph of a linear
More informationAppendix M TERMINOLOGY. Slope of a Line. Slope. Undefined Slope. Slope-Intercept Form
Appendices : Slope of a Line TERMINOLOGY For each of the following terms, provide ) a definition in our own words, 2) the formal definition (as provided b our text or instructor), and ) an example of the
More informationGraphs of linear equations will be perfectly straight lines. Why would we say that A and B are not both zero?
College algebra Linear Functions : Definition, Horizontal and Vertical Lines, Slope, Rate of Change, Slopeintercept Form, Point-slope Form, Parallel and Perpendicular Lines, Linear Regression (sections.3
More informationSlope-Intercept Form. Find the x- and y-intercepts. 1. y 3x 6 2. y 2x 8. Graph each equation. 3. y 1 x 3 4. y 5x 5 5. y x 4
Practice A Slope-Intercept Form Find the x- and y-intercepts. 1. y 3x 6. y x 8 _ Graph each equation. 3. y 1 x 3 4. y 5x 5 5. y x 4 Write the equation of the line in slope-intercept form. 6. 7. _ Practice
More informationParallel and Perpendicular Lines on the Coordinate Plane
Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane 1.5 Learning Goals Key Term In this lesson, you will: Determine whether lines are parallel. Identify and write the
More informationCh. 6 Linear Functions Notes
First Name: Last Name: Block: Ch. 6 Linear Functions Notes 6.1 SLOPE OF A LINE Ch. 6.1 HW: p. 9 #4 1, 17,,, 8 6. SLOPES OF PARALLEL AND PERPENDICULAR LINES 6 Ch. 6. HW: p. 49 # 6 odd letters, 7 0 8 6.
More informationFind the equation of a line given its slope and y-intercept. (Problem Set exercises 1 6 are similar.)
Directions Each problem below is similar to the example with the same number in your textbook. After reading through an example in your textbook, or watching one of the videos of that example on MathTV,
More informationRoots of Quadratic Functions
LESSON 12 Roots of Quadratic Functions LEARNING OBJECTIVES Today I am: sketching parabolas with limited information. So that I can: identify the strengths of each form of a quadratic equation. I ll know
More informationAlgebra & Trig. 1. , then the slope of the line is given by
Algebra & Trig. 1 1.4 and 1.5 Linear Functions and Slope Slope is a measure of the steepness of a line and is denoted by the letter m. If a nonvertical line passes through two distinct points x, y 1 1
More informationDetermine the intercepts of the line and ellipse below: Definition: An intercept is a point of a graph on an axis. Line: x intercept(s)
Topic 1 1 Intercepts and Lines Definition: An intercept is a point of a graph on an axis. For an equation Involving ordered pairs (x, y): x intercepts (a, 0) y intercepts (0, b) where a and b are real
More informationChapter 7 Graphing Equations of Lines and Linear Models; Rates of Change Section 3 Using Slope to Graph Equations of Lines and Linear Models
Math 167 Pre-Statistics Chapter 7 Graphing Equations of Lines and Linear Models; Rates of Change Section 3 Using Slope to Graph Equations of Lines and Linear Models Objectives 1. Use the slope and the
More informationPractice 5-6. Linear Equations y = mx + b. Name Class Date
Name Class Date Practice 5-6 Linear Equations y = mx + b 5-6 Linear Equations y = mx + b 1. Write an equation for the line in slope-intercept form. Use integers or 2. Write an equation for the line in
More informationMathematics Success Grade 8
T936 Mathematics Success Grade 8 [OBJECTIVE] The student will find the line of best fit for a scatter plot, interpret the equation and y-intercept of the linear representation, and make predictions based
More informationAdditional Practice. Name Date Class
Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Name Date Class Additional Practice Investigation For Eercises 1 4, write an equation and sketch a graph for the line
More informationLesson 24: Finding x-intercepts Again?
Opening Discussion The quadratic function, y = x 2 6x + 8, can be written as y = (x 2)(x 4) and as y = (x 3) 2 1. Deshi and Ame wanted to find the x-intercepts of this function. Their work is shown below.
More informationInvestigating Intercepts
Unit: 0 Lesson: 01 1. Can more than one line have the same slope? If more than one line has the same slope, what makes the lines different? a. Graph the following set of equations on the same set of aes.
More informationLesson 4.6 Best Fit Line
Lesson 4.6 Best Fit Line Concept: Using & Interpreting Best Fit Lines EQs: -How do we determine a line of best fit from a scatter plot? (S.ID.6 a,c) -What does the slope and intercept tell me about the
More informationUnit 5: Moving Straight Ahead
Unit 5: Moving Straight Ahead Investigation 4 Exploring Slope: Connecting Rates and Ratios I can demonstrate understanding that linear relationships are relationships represented by the slope of the line
More informationAlgebra 1B. Chapter 6: Linear Equations & Their Graphs Sections 6-1 through 6-7 & 7-5. COLYER Fall Name: Period:
Chapter 6: Linear Equations & Their Graphs Sections 6-1 through 6-7 & 7-5 COLYER Fall 2016 Name: Period: What s the Big Idea? Analyzing Linear Equations & Inequalities What can I expect to understand when
More informationUnit 1 Introduction to Precalculus Linear Equations in Two Variables (Unit 1.3)
Unit 1 Introduction to Precalculus Linear Equations in Two Variables (Unit 1.3) William (Bill) Finch Mathematics Department Denton High School Lesson Goals When ou have completed this lesson ou will: Find
More informationSlope. Plug In. Finding the Slope of a Line. m 5 1_ 2. The y-intercept is where a line
LESSON Slope Plug In Finding the Slope of a Line The slope of a line is the ratio of the change in the -values to the change in the corresponding -values. 0 7 8 change in -values Slope change in -values
More informationEquations of Parallel and Perpendicular Lines
COMMON CORE AB is rise - - 1 - - 0 - - 8 6 Locker LESSON. Equations of Parallel and Perpendicular Lines Name Class Date. Equations of Parallel and Perpendicular Lines Essential Question: How can ou find
More informationMS Algebra A-F-IF-7 Ch. 5.6a Graph Using Slope-Intercept Form. Mr. Deyo Graph Using Slope-Intercept Form
MS Algebra A-F-IF-7 Ch. 5.6a Graph Using Slope-Intercept Form Mr. Deyo Graph Using Slope-Intercept Form Title: 5.6a Slope-Intercept Form Date: Learning Target By the end of the period, I will apply the
More informationReview for Mastery. Identifying Linear Functions
Identifying Linear Functions You can determine if a function is linear by its graph, ordered pairs, or equation. Identify whether the graph represents a linear function. Step 1: Determine whether the graph
More informationLogarithms. Since perhaps it s been a while, calculate a few logarithms just to warm up.
Logarithms Since perhaps it s been a while, calculate a few logarithms just to warm up. 1. Calculate the following. (a) log 3 (27) = (b) log 9 (27) = (c) log 3 ( 1 9 ) = (d) ln(e 3 ) = (e) log( 100) =
More informationManchester College Education Department. Lesson Plan by Daniel Haffner
Manchester College Education Department Lesson Plan by Daniel Haffner Lesson: Quiz on Slope, Slope-Intercept Form, and Standard Form Length: 70 min Age or Grade Level Intended: Algebra 1 Academic Standard(s):
More informationSection 2-4: Writing Linear Equations, Including Concepts of Parallel & Perpendicular Lines + Graphing Practice
Section 2-4: Writing Linear Equations, Including Concepts of Parallel & Perpendicular Lines + Graphing Practice Name Date CP If an equation is linear, then there are three formats typically used to express
More informationLesson 7A Slope-Intercept Formula
Lesson 7A Slope-Intercept Formula Terms Two new words that describe what we've been doing in graphing lines are slope and intercept. The slope is referred to as "m" (a mountain has slope and starts with
More informationGraphs, Linear Equations and Functions
Graphs, Linear Equations and Functions There are several ways to graph a linear equation: Make a table of values Use slope and y-intercept Use x and y intercepts Oct 5 9:37 PM Oct 5 9:38 PM Example: Make
More informationE. Slope-Intercept Form and Direct Variation (pp )
and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the
More informationSlopes of of Parallel and and Perpendicular Lines Lines Holt Algebra 1
5-8 Slopes of of Parallel and and Lines Warm Up Lesson Presentation Lesson Quiz Bell Quiz 5-8 Find the reciprocal. 1. 2 2. 1 pt 1 pt 1 pt 3. 2 pts 2 pts 2 pts Find the slope of the line that passes through
More informationThe Picture Tells the Linear Story
The Picture Tells the Linear Story Students investigate the relationship between constants and coefficients in a linear equation and the resulting slopes and y-intercepts on the graphs. This activity also
More informationLINEAR EQUATIONS IN TWO VARIABLES
LINEAR EQUATIONS IN TWO VARIABLES What You Should Learn Use slope to graph linear equations in two " variables. Find the slope of a line given two points on the line. Write linear equations in two variables.
More informationHorizontal and Vertical Lines. 1. Consider the equation, y 5 26, that you wrote for the table shown in the previous activity.
ACTIVITY 5. Horizontal and Vertical Lines Horizontal and vertical lines represent linear relationships, but their equations are different from the equations of lines that are not horizontal or vertical.
More informationGraphing Lines with a Table
Graphing Lines with a Table Select (or use pre-selected) values for x Substitute those x values in the equation and solve for y Graph the x and y values as ordered pairs Connect points with a line Graph
More information6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line.
6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line. Toolkit: - Rate of change - Simplifying fractions Main Ideas: Definitions Rise: the vertical distance between two
More information6.1 Slope-Intercept Form
Name Class Date 6.1 Slope-Intercept Form Essential Question: How can ou represent a linear function in a wa that reveals its slope and -intercept? Resource Locker Eplore Graphing Lines Given Slope and
More informationACT Coordinate Geometry Review
ACT Coordinate Geometry Review Here is a brief review of the coordinate geometry concepts tested on the ACT. Note: there is no review of how to graph an equation on this worksheet. Questions testing this
More informationMath 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004
Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004 Every vertical line can be expressed by a unique equation of the form x = c, where c is a constant. Such lines have undefined
More informationUnit 11: Linear Equations
Section 11.1: General Form: ax + by = c Section 11.2: Applications General Form Section 11.3: Point-Slope Form: y y 1 = m(x x 1 ) KEY TERMS AND CONCEPTS Look for the following terms and concepts as you
More informationAim #35.1: How do we graph using a table?
A) Take out last night's homework Worksheet - Aim 34.2 B) Copy down tonight's homework Finish aim 35.1 Aim #35.1: How do we graph using a table? C) Plot the following points... a) (-3, 5) b) (4, -2) c)
More informationOutcome 9 Review Foundations and Pre-Calculus 10
Outcome 9 Review Foundations and Pre-Calculus 10 Level 2 Example: Writing an equation in slope intercept form Slope-Intercept Form: y = mx + b m = slope b = y-intercept Ex : Write the equation of a line
More informationChapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane
Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant
More information2.3 Quick Graphs of Linear Equations
2.3 Quick Graphs of Linear Equations Algebra III Mr. Niedert Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 1 / 11 Forms of a Line Slope-Intercept Form The slope-intercept form of a linear
More informationMA Lesson 16 Sections 2.3 and 2.4
MA 1500 Lesson 16 Sections.3 and.4 I Piecewise Functions & Evaluating such Functions A cab driver charges $4 a ride for a ride less than 5 miles. He charges $4 plus $0.50 a mile for a ride greater than
More information3-6. Lines in the Coordinate Plane Going Deeper E X A M P L E. Slope-Intercept Form. Point-Slope Form. Writing Equations of Parallel Lines
Name Class Date 3-6 Lines in the Coordinate Plane Going Deeper Essential question: How can you use slope to write equations of lines that are parallel or perpendicular? Recall that a linear function can
More informationChapter 2: Linear Equations/Inequalities of two variables
Chapter 2: Linear Equations/Inequalities of two variables I. Introduction to the Rectangular (Cartesian) Coordinate System II. Linear Equations in 2-variables III. Graphing Using Intercepts IV. Two Special
More informationLesson 15: The Slope of a Non Vertical Line
Classwork Opening Exercise Example Graph A Graph B a. Which graph is steeper? b. Write directions that explain how to move from one point on the graph to the other for each of Graph A and Graph B. c. Write
More informationFactored Form When a = 1
Lesson 4 Hart Interactive Algebra Lesson 4: Factored Form When a = Opening Activity Graph Exchange Your group will need: one quadratic graph. A. For your given graph, circle the graph number on the table
More informationNOTES: Chapter 6 Linear Functions
NOTES: Chapter 6 Linear Functions Algebra 1-1 COLYER Fall 2016 Student Name: Page 2 Section 6.1 ~ Rate of Change and Slope Rate of Change: A number that allows you to see the relationship between two quantities
More informationScatter Plots, Correlation, and Lines of Best Fit
Lesson 7.3 Objectives Interpret a scatter plot. Identify the correlation of data from a scatter plot. Find the line of best fit for a set of data. Scatter Plots, Correlation, and Lines of Best Fit A video
More informationParallel and Perpendicular Lines on the Coordinate Plane
Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane 1.5 Learning Goals Key Term In this lesson, you will: Determine whether lines are parallel. Identify and write the
More informationLesson 11: Linear and Exponential Investigations
Hart Interactive Algebra Lesson Lesson : Linear and Exponential Investigations Opening Exercise In this lesson, you ll be exploring linear and exponential function in five different investigations. You
More informationSection 7.2 Logarithmic Functions
Math 150 c Lynch 1 of 6 Section 7.2 Logarithmic Functions Definition. Let a be any positive number not equal to 1. The logarithm of x to the base a is y if and only if a y = x. The number y is denoted
More informationPage 1 of 1-7 Equations Teks Focus TEKS (2)(B) Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity
More informationLesson 1b Linear Equations
In the first lesson we looked at the concepts and rules of a Function. The first Function that we are going to investigate is the Linear Function. This is a good place to start because with Linear Functions,
More information3.4 and 4.3 Explain Graphing and Writing Linear Equations in Standard Form - Notes
3.4 and 4.3 Explain Graphing and Writing Linear Equations in Standard Form - Notes Essential Question: How can you describe the graph of the equation Ax + By = C? How can you write the equation of a line
More informationLesson 16. Opening Exploration A Special Case
Opening Exploration A Special Case 1. Consuela ran across the quadratic equation y = 4x 2 16 and wondered how it could be factored. She rewrote it as y = 4x 2 + 0x 16. A. Use one of the methods you ve
More informationChapter 2: Functions and Graphs Lesson Index & Summary
Section 1: Relations and Graphs Cartesian coordinates Screen 2 Coordinate plane Screen 2 Domain of relation Screen 3 Graph of a relation Screen 3 Linear equation Screen 6 Ordered pairs Screen 1 Origin
More informationLesson 11: Linear Functions, Part 2
Lesson 11 continues the study of linear functions. In this lesson, we look at how to write linear equations in slope-intercept and general form and applications where these may be used. We also look at
More information4.5 Equations of Parallel and Perpendicular Lines
Name Class Date.5 Equations of Parallel and Perpendicular Lines Essential Question: How can ou find the equation of a line that is parallel or perpendicular to a given line? Resource Locker Eplore Eploring
More information1 Write a Function in
www.ck12.org Chapter 1. Write a Function in Slope-Intercept Form CHAPTER 1 Write a Function in Slope-Intercept Form Here you ll learn how to write the slope-intercept form of linear functions and how to
More informationCONSTANT RATE OF CHANGE & THE POINT-SLOPE FORMULA
CONSTANT RATE OF CHANGE & THE POINT-SLOPE FORMULA 1. In Worksheet 3 we defined the meaning of constant rate of change. a. Explain what it means for two quantities to be related by a constant rate of change.
More informationSolving Equations and Graphing
Solving Equations and Graphing Question 1: How do you solve a linear equation? Answer 1: 1. Remove any parentheses or other grouping symbols (if necessary). 2. If the equation contains a fraction, multiply
More informationLesson 16: The Computation of the Slope of a Non Vertical Line
++ Lesson 16: The Computation of the Slope of a Non Vertical Line Student Outcomes Students use similar triangles to explain why the slope is the same between any two distinct points on a non vertical
More informationRegression: Tree Rings and Measuring Things
Objectives: Measure biological data Use biological measurements to calculate means, slope and intercept Determine best linear fit of data Interpret fit using correlation Materials: Ruler (in millimeters)
More informationUNIT #4 LINEAR FUNCTIONS AND ARITHMETIC SEQUENCES REVIEW QUESTIONS
Name: Date: UNIT # LINEAR FUNCTIONS AND ARITHMETIC SEQUENCES REVIEW QUESTIONS Part I Questions. Carl walks 30 feet in seven seconds. At this rate, how man minutes will it take for Carl to walk a mile if
More informationStudy Guide and Review - Chapter 3. Find the x-intercept and y-intercept of the graph of each linear function.
Find the x-intercept and y-intercept of the graph of each linear function. 11. The x-intercept is the point at which the y-coordinate is 0, or the line crosses the x-axis. So, the x-intercept is 8. The
More informationSupplemental Worksheet Problems To Accompany: The Algebra 2 Tutor Section 4 Graphing Inequalities
Supplemental Worksheet Problems To Accompan: The Algebra Tutor Please watch Section 4 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item9.cfm Sample
More informationNovember 28, scatterplots and lines of fit ink.notebook. Page 153. Page 154. Page Scatter Plots and Line of Fit.
. scatterplots and lines of fit ink.notebook Page Page Page. Scatter Plots and Line of Fit Page Page 6 Page 7 . scatterplots and lines of fit ink.notebook Lesson Objectives Standards Lesson Notes Lesson
More informationHomework 5 - Section 3.3 #5
Homework 5 - Section. #5 Intermediate Algebra / MAT 15 Fall 01 possible master (Prof. Fleischner) Student Name/ID: 1. Rewrite the equation in A + B = C form. Use integers for A, B, and C. + 5 = +. Rewrite
More information3.4 The Slope of a Line
CHAPTER Graphs and Functions. The Slope of a Line S Find the Slope of a Line Given Two Points on the Line. Find the Slope of a Line Given the Equation of a Line. Interpret the Slope Intercept Form in an
More informationLesson 8. Diana Pell. Monday, January 27
Lesson 8 Diana Pell Monday, January 27 Section 5.2: Continued Richter scale is a logarithmic scale used to express the total amount of energy released by an earthquake. The Richter scale gives the magnitude
More informationExploring bivariate data Student Activity Sheet 4; use with Exploring Interpreting linear models
1. What is Hooke s Law? 2. What item in the science experiment is being used to simulate a spring? 3. Fill in the table (for number of marbles = {0, 5, 10, 15}) with the data collected during the science
More informationPlotting Points in 2-dimensions. Graphing 2 variable equations. Stuff About Lines
Plotting Points in 2-dimensions Graphing 2 variable equations Stuff About Lines Plotting Points in 2-dimensions Plotting Points: 2-dimension Setup of the Cartesian Coordinate System: Draw 2 number lines:
More informationVOCABULARY WORDS. quadratic equation root(s) of an equation zero(s) of a function extraneous root quadratic formula discriminant
VOCABULARY WORDS quadratic equation root(s) of an equation zero(s) of a function extraneous root quadratic formula discriminant 1. Each water fountain jet creates a parabolic stream of water. You can represent
More information8.EE. Development from y = mx to y = mx + b DRAFT EduTron Corporation. Draft for NYSED NTI Use Only
8.EE EduTron Corporation Draft for NYSED NTI Use Only TEACHER S GUIDE 8.EE.6 DERIVING EQUATIONS FOR LINES WITH NON-ZERO Y-INTERCEPTS Development from y = mx to y = mx + b DRAFT 2012.11.29 Teacher s Guide:
More informationUNIT 2 LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set 2: Relations Versus Functions/Domain and Range
UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Relations Versus Functions/Domain and Range Station You will be given a ruler and graph paper. As a group, use our ruler to determine
More informationUsing Slopes and Intercepts
CODE Name Date Teacher Practice A Using Slopes and Intercepts 1. Name the ordered pair if the x-intercept is 2. 2. Name the ordered pair if the y-intercept is 8. 3. In the ordered pair (9, 0), what is
More informationDetermine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. y = 4x + 3
Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. y = 4x + 3 Rewrite the equation in standard form. The equation is now in standard form
More informationMS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points. ALGEBRA SUPPORT Day 1 of 2 Find Slope and Rate of Change
MS Algebra ASID7 Ch. 5.5a Find Slope Given Two Points ALGEBRA SUPPORT Day 1 of 2 Find Slope and Rate of Change Title: 5.5a Find Slope Given Two Points Day 1 of 2 Date: SUPPORT Class Learning Target By
More informationA slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
The Slope of a Line (2.2) Find the slope of a line given two points on the line (Objective #1) A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
More informationDiscovery Activity: Slope
Page 1 of 14 1. Lesson Title: Discovering Slope-Intercept Form 2. Lesson Summary: This lesson is a review of slope and guides the students through discovering slope-intercept form using paper/pencil and
More informationStudent Exploration: Standard Form of a Line
Name: Date: Student Exploration: Standard Form of a Line Vocabulary: slope, slope-intercept form, standard form, x-intercept, y-intercept Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1.
More informationLesson 3A. Opening Exercise. Identify which dilation figures were created using r = 1, using r > 1, and using 0 < r < 1.
: Properties of Dilations and Equations of lines Opening Exercise Identify which dilation figures were created using r = 1, using r > 1, and using 0 < r < 1. : Properties of Dilations and Equations of
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 informationSlope-Intercept Form of a Line
Lesson Plan Lecture Edition Slope-Intercept Form of a Line Objectives Students will: discover how slope effects the graph of a line. relate b to the y-intercept of a line. determine the equation of a line
More informationLesson 2.1 Linear Regression
Lesson 2.1 Linear Regression Activity 1 Line of Best Fit The scatterplot shows the area, E, of the Amazon rain forest remaining, in thousands of square kilometers, > years after 1980. > E 6 3745 8 3724
More information4 The Cartesian Coordinate System- Pictures of Equations
The Cartesian Coordinate System- Pictures of Equations Concepts: The Cartesian Coordinate System Graphs of Equations in Two Variables x-intercepts and y-intercepts Distance in Two Dimensions and the Pythagorean
More informationBlock: Date: Name: REVIEW Linear Equations. 7.What is the equation of the line that passes through the point (5, -3) and has a slope of -3?
Name: REVIEW Linear Equations 1. What is the slope of the line y = -2x + 3? 2. Write the equation in slope-intercept form. Block: Date: 7.What is the equation of the line that passes through the point
More informationCH 54 SPECIAL LINES. Ch 54 Special Lines. Introduction
479 CH 54 SPECIAL LINES Introduction Y ou may have noticed that all the lines we ve seen so far in this course have had slopes that were either positive or negative. You may also have observed that every
More informationLesson 7 Slope-Intercept Formula
Lesson 7 Slope-Intercept Formula Terms Two new words that describe what we've been doing in graphing lines are slope and intercept. The slope is referred to as "m" (a mountain has slope and starts with
More informationChapter 3 Exponential and Logarithmic Functions
Chapter 3 Exponential and Logarithmic Functions Section 1 Section 2 Section 3 Section 4 Section 5 Exponential Functions and Their Graphs Logarithmic Functions and Their Graphs Properties of Logarithms
More information