Section 2.2 Intercepts & Symmetry
|
|
- Esther Lindsey
- 5 years ago
- Views:
Transcription
1 Section 2.2 Intercepts & Symmetry Intercepts Week 2 Handout MAC 1105 Professor Niraj Wagh J The x-intercept(s) of an equation on a graph is the point on the graph where y = 0. è So to find the x-intercept, let y = 0. The y-intercept(s) of an equation on a graph is the point on the graph where x = 0. è So to find the y-intercept, let x = 0. Symmetry X-Axis Symmetry A graph is said to be symmetric about the x-axis if, for every point (x, y) on the graph, the point (x, -y) is also on the graph. è To test if the graph of an equation is symmetric about the x-axis, replace y with negative y and simplify. If the same equation exists then it is symmetric about the x-axis. Y-Axis Symmetry A graph is said to be symmetric about the y-axis if, for every point (x, y) on the graph, the point (-x, y) is also on the graph. è To test if the graph of an equation is symmetric about the y-axis, replace x with negative x and simplify. If the same equation exists then it is symmetric about the y-axis. N. Wagh 1
2 Origin Symmetry A graph is said to be symmetric about the origin if, for every point (x, y) on the graph, the point (-x, -y) is also on the graph. è To test if the graph of an equation is symmetric about the origin, replace both x with negative x and y with negative y and simplify. If the same equation exists then it is symmetric about the origin. 2.2 Example (a) (b) (c) Decide if the points (0, 0), (7, 4), or (1, 5) are solutions to the equation. Find the x and y-intercepts. Decide if the equation exhibits x, y, or origin symmetry. 1. y $ = x + 9 N. Wagh 2
3 Section 2.3 Lines Slope Let P 1 = (x 1, y 1 ) and P 2 = (x 2, y 2 ) be two distinct points. The slope m containing P 1 and P 2 is: m = rise run m = y 2 y 1 OR m = y 1 y 2 x 2 x 1 x 1 x 2 N. Wagh 3
4 Notes: If x 1 = x 2, the slope of the line will be undefined since we cannot divide by zero. è The resulting line is vertical. (UNDEFINED SLOPE, Form: X = some #) Mr. Penguin: AHH!!! HELP ME!! L If y 1 = y 2, the slope of the line will be 0 and zero divided by anything will be zero. è The resulting line is horizontal. (NO SLOPE, Form: Y = some #) Mr. Penguin: Umm.. I m not going anywhere, this is boring! N. Wagh 4
5 Positive Slope Mr. Penguin: I m tired. Negative Slope Mr. Penguin: Weee!!!! Credits for images: themathroundtable.wikispaces.com/speedo's+page Forms of Equations of Lines Slope-Intercept Form of an Equation of a Line An equation with slope m and y-intercept b is y = mx + b Point-Slope Form of an Equation of a Line An equation of a non-vertical line with slope m that contains point (x 1, y 1 ) is General Form of an Equation of a Line y y 1 = m(x x 1 ) Ax + By = C Where A, B, and C are real numbers and A and B are not both 0. N. Wagh 5
6 Parallel Lines Two nonvertical lines are said to parallel with one another if and only if they have the same slope and different y-intercepts. è Have the same slope. è Have different y-intercepts. NOTE: If the lines had the same y-intercept they would be the same line. :P Perpendicular Lines Two nonvertical lines are perpendicular (when two lines intersect at a right angle [90 0 ]) if and only if the product of their slopes is -1. NOTE: You can also say that two nonvertical lines are perpendicular if the slopes are negative reciprocals of one another. è For example, if one line had a slope of 5 and the other line had a slope of -1/5 then they are perpendicular lines. o This is because 5*-1/5 = -1. J 2.3 Examples Find an equation for the line with the given properties. Express your answers using slope-intercept form. 1. Containing the points (-3, 4) and (2, 5) N. Wagh 6
7 2. Parallel and Perpendicular to the line y = 2x 3; containing the point (1, -2) 3. Gloria loves going to concerts. Her favorite artist is Kendrick Lamar. When she heard Kendrick was coming to town she knew she had to go! She wants to meet Kendrick so she buys a meet and greet pass for 499 dollars plus 6 dollars for each type of merchandise she buys. Write a linear equation that relates the cost C, in dollars, of buying a ticket to the number x of merchandise she buys. What is the total cost of the concert if Gloria gets 5 types of merchandise? 10 types of merchandise? N. Wagh 7
8 PRACTICE. PRACTICE. PRACTICE. 1. y 5x $ = 4 (a) (b) (c) Decide if the points (0, 4), (1, 3), or (3, 3) are solutions to the equation. Find the x and y-intercepts. Decide if the equation exhibits x, y, or origin symmetry. 2. Find an equation that is perpendicular to y = -4x + 10 that passes through the point (7, 2). 3. Find an equation that goes through the points (2, 5) and (10, 1). We are done! Now work on HW 2.2, 2.3. If you have any questions, please let me know! N. Wagh 8
9 Section 2.4 Circles A circle is a set of points in the xy-plane that are a fixed distance r from a fixed point (h, k). The fixed distance r is called the radius, and the fixed point (h, k) is called the center of the circle. Forms The standard form of an equation of a circle with radius r and center (h, k) is (x h) 2 + (y k) 2 = r 2 The general form of the equation of a circle is x 2 + y 2 + ax + by + c = 0 Hey I m a circle too! N. Wagh 9
10 Completing The Square Steps Use this technique to factor the general form. è Recall the general form of the equation of a circle is x 2 + y 2 + ax + by + c = 0 1. Make sure that the coefficients for x 2 and y 2 are Rearrange so that you get the form: (x 2 + ax)+ (y 2 + by) = c 3. Take half of the a and b term, these are the coefficients of the x and y terms respectively. 4. Square those numbers and add it each respective number within the parentheses. 5. Now add the numbers to the other side of the equation. 6. Factor each and simplify. 2.4 Examples Write the standard and general form of the equation of each circle of radius r and center (h, k). Then graph the circle. 1. r = 3; (h, k) = (0, 0) N. Wagh 10
11 First, find the center (h, k) and radius of the circle. Second, graph the circle. And lastly, find the intercepts, if any. 2. 3x 2 + 3y 2 24x + 6y 24 = 0 N. Wagh 11
12 PRACTICE. PRACTICE. PRACTICE. 3. x 2 + y 2 + 4x + 2y 20 = 0 4. x 2 + y 2 6x 8y 11= 0 5. x 2 + y 2 4x 6y 23 = 0 6. x 2 + y 2 3x + 4y + 4 = x 2 + 5y 2 30x +10y 75 = 0 Yay! Now work on HW 2.4. If you have any questions, please let me know! N. Wagh 12
Sections 3.2 & 3.3 Introduction to Functions & Graphing
Week 4 Handout MAT 1033C Professor Niraj Wagh J Sections 3.2 & 3.3 Introduction to Functions & Graphing Function A function f is a rule that assigns to each element x in a set A exactly one element, called
More informationSection 3.2 Quadratic Functions & Their Graphs
Week 2 Handout MAC 1140 Professor Niraj Wagh J Section 3.2 Quadratic Functions & Their Graphs Quadratic Function: Standard Form A quadratic function is a function that can be written in the form: f (x)
More informationSect The Slope-Intercept Form
0 Concepts # and # Sect. - The Slope-Intercept Form Slope-Intercept Form of a line Recall the following definition from the beginning of the chapter: Let a, b, and c be real numbers where a and b are not
More informationAverage Rate of Change & Slope of a Line MATH 092
Average Rate of Change Average Rate of Change & Slope of a Line MATH 092 Functions are used to model the way one quantity changes with respect to another quantity. For instance, how does the distance traveled
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in
More informationB. Linear equations can be written in the form y = mx+b or f(x) = mx+b. which is called: Or Ax + By = C which is called:
Math 95, Mod 1, Sec. 3.3 Graphing Linear functions A. Graphing Linear functions E. 1: Graph: f() = 3, g() = 3 + 2 and h() = 3-3 f() g() h() 0-2 2 What happens? B. Linear equations can be written in the
More informationSection 1.6. Functions
Section 1.6 Functions Definitions Relation, Domain, Range, and Function The table describes a relationship between the variables x and y. This relationship is also described graphically. x y 3 2 4 1 5
More informationSlope Intercept form. Complete the graph below and write the equation of the line. Then, answer questions a-d.
Chapter 5: Writing Linear Equations Name: Section 5.1: Write Linear Equations in Slope-Intercept Form Slope Intercept form Complete the graph below and write the equation of the line. Then, answer questions
More informationPre-AP Algebra II Summer Packet 2014
Pre-AP Algebra II Summer Packet 014 Name: Period: PLEASE READ THE FOLLOWING!!!!!!! Wait until a few weeks before school starts to work through this packet so that the material will be fresh when you begin
More informationMath M111: Lecture Notes For Chapter 3
Section 3.1: Math M111: Lecture Notes For Chapter 3 Note: Make sure you already printed the graphing papers Plotting Points, Quadrant s signs, x-intercepts and y-intercepts Example 1: Plot the following
More informationCartesian Plane. Analytic Geometry. Unit Name
3.1cartesian Unit Name Analytic Geometry Unit Goals 1. Create table of values in order to graph &/or determine if a relation is linear. Determine slope 3. Calculate missing information for linearelationships.
More informationMathematics Department Columbia High School. Advanced Algebra 2 Summer Packet
Mathematics Department Columbia High School Advanced Algebra Summer Packet This summer packet is for students entering Advanced Algebra (10-5) for the Fall. The material contained in this packet represents
More informationSOLUTIONS FOR PROBLEMS 1-30
. Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).
More informationMini Lecture 2.1 Introduction to Functions
Mini Lecture.1 Introduction to Functions 1. Find the domain and range of a relation.. Determine whether a relation is a function. 3. Evaluate a function. 1. Find the domain and range of the relation. a.
More informationLESSON EII.F ABSOLUTE VALUE 89
LESSON EII.F ABSOLUTE VALUE LESSON EII.F ABSOLUTE VALUE 89 OVERVIEW Here s what you ll learn in this lesson: Solving Equations a. Solving x = a b. Solving Ax + B = a c. Solving Ax + B = Cx + D Solving
More informationJune If you want, you may scan your assignment and convert it to a.pdf file and it to me.
Summer Assignment Pre-Calculus Honors June 2016 Dear Student: This assignment is a mandatory part of the Pre-Calculus Honors course. Students who do not complete the assignment will be placed in the regular
More informationReteach 2-3. Graphing Linear Functions. 22 Holt Algebra 2. Name Date Class
-3 Graphing Linear Functions Use intercepts to sketch the graph of the function 3x 6y 1. The x-intercept is where the graph crosses the x-axis. To find the x-intercept, set y 0 and solve for x. 3x 6y 1
More informationANSWER KEY. Checklist Do I understand? Test Date: A-Day 2/7. Algebra 1 Benchmark Review study guide is due on test day!
ANSWER KEY Name: Algebra 1 Benchmark Review study guide is due on test day! Test Date: A-Day 2/7 Checklist Do I understand? Unit 1 Solving Equations and Inequalities Two Step Equations Properties of Real
More informationChapter One: Pre-Geometry
Chapter One: Pre-Geometry Index: A: Solving Equations B: Factoring (GCF/DOTS) C: Factoring (Case Two leading into Case One) D: Factoring (Case One) E: Solving Quadratics F: Parallel and Perpendicular Lines
More informationChapter 5: Writing Linear Equations Study Guide (REG)
Chapter 5: Writing Linear Equations Study Guide (REG) 5.1: Write equations of lines given slope and y intercept or two points Write the equation of the line with the given information: Ex: Slope: 0, y
More information2. The table of values shows the cost of movie tickets at a local theatre.
Relations and Functions Practice Questions. The following distance-time graph represents the distance (in kilometres) a person bicycled during a 0-min period. Describe a possible scenario. 6 d (km) 6 9
More informationChapter 3: Inequalities, Lines and Circles, Introduction to Functions
QUIZ AND TEST INFORMATION: The material in this chapter is on Quiz 3 and Exam 2. You should complete at least one attempt of Quiz 3 before taking Exam 2. This material is also on the final exam and used
More informationUnit 3: Writing Linear Equations
Unit 3: Writing Linear Equations Name: SUCCESS CRITERIA FOR WRITING AN EQUATION IN SLOPE-INTERCEPT FORM (y = mx + b) SUCCESS CRITERIA FOR WRITING AN EQUATION IN STANDARD FORM (Ax + By = C) 1 Slope Intercept
More informationElementary Algebra Sample Final Exam Spring 2017
Elementary Algebra NAME: Sample Final Exam Spring 2017 You will have 2 hours to complete this exam. You may use a calculator but must show all algebraic work in the space provided to receive full credit.
More informationMAC College Algebra
MAC 05 - College Algebra Name Review for Test 2 - Chapter 2 Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact distance between the
More informationLHS June 2012 Algebra 1 Final Exam
Teacher: (circle one) Mrs. Gordon Mr. Normile E-block Mr. Normile F-block LHS June 2012 Algebra 1 Final Exam Multiple Choice + Short Answer = /65 Part I Multiple Choice 33 questions 33 points This is a
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 informationMAC 1105-College Algebra LSCC, S. Nunamaker
MAC 1105-College Algebra LSCC, S. Nunamaker Chapter 1-Graphs, Functions, and Models 1.1 Introduction to Graphing I. Reasons for using graphs A. Visual presentations enhance understanding. B. Visual presentations
More information3.3 Linear Equations in Standard Form
3.3 Linear Equations in Standard Form Learning Objectives Write equivalent equations in standard form. Find the slope and y intercept from an equation in standard form. Write equations in standard form
More informationChapter 1: Precalculus Review
: Precalculus Review Math 115 17 January 2018 Overview 1 Important Notation 2 Exponents 3 Polynomials 4 Rational Functions 5 Cartesian Coordinates 6 Lines Notation Intervals: Interval Notation (a, b) (a,
More informationSummer Packet Pre-AP Algebra
Name: (5/11/17) Summer Packet Pre-AP Algebra 1-2018-19 To receive credit all work must be shown. There will be a test the first week back from summer on this packet. Any work done on additional paper must
More information4 The Cartesian Coordinate System- Pictures of Equations
4 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
More information9.7 Extension: Writing and Graphing the Equations
www.ck12.org Chapter 9. Circles 9.7 Extension: Writing and Graphing the Equations of Circles Learning Objectives Graph a circle. Find the equation of a circle in the coordinate plane. Find the radius and
More informationUse slope and y-intercept to write an equation. Write an equation of the line with a slope of 1 } 2. Write slope-intercept form.
5.1 Study Guide For use with pages 282 291 GOAL Write equations of lines. EXAMPLE 1 Use slope and y-intercept to write an equation Write an equation of the line with a slope of 1 } 2 and a y-intercept
More informationCharacteristics of Linear Functions (pp. 1 of 8)
Characteristics of Linear Functions (pp. 1 of 8) Algebra 2 Parent Function Table Linear Parent Function: x y y = Domain: Range: What patterns do you observe in the table and graph of the linear parent
More informationTable of contents. Jakayla Robbins & Beth Kelly (UK) Precalculus Notes Fall / 53
Table of contents The Cartesian Coordinate System - Pictures of Equations Your Personal Review Graphs of Equations with Two Variables Distance Equations of Circles Midpoints Quantifying the Steepness of
More informationMock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}
Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the
More informationGeometry Summer Assignment 2018
Geometry Summer Assignment 2018 The following packet contains topics and definitions that you will be required to know in order to succeed in Geometry this year. You are advised to be familiar with each
More informationRegents Review Session #3 Functions
Regents Review Session #3 Functions A relation is a set of ordered pairs. A function is a relation in which each element of the domain corresponds t exactly one element in the range. (Each x value is paired
More informationSolutions to MAT 117 Test #1
Solutions to MAT 117 Test #1 Because there are two versions of the test, solutions will only be given for Form A. Differences from the Form B version will be given. (The values for Form A appear above
More informationPractice Test 4: Linear Relations
AChor/MFMP : Linear Relations K: C: A: T: PART A: Multiple Choice Questions Instructions: Circle the English letter of the best answer. Circle one and ONLY one answer for each question. PART B: FULL SOLUTION
More informationSection 1.4 Circles. Objective #1: Writing the Equation of a Circle in Standard Form.
1 Section 1. Circles Objective #1: Writing the Equation of a Circle in Standard Form. We begin by giving a definition of a circle: Definition: A Circle is the set of all points that are equidistant from
More informationEquation. A mathematical sentence formed by setting two expressions equal to each other. Example 1: 3 6 = 18 Example 2: 7 + x = 12
Equation A mathematical sentence formed by setting two expressions equal to each other Example 1: 3 6 = 18 Example 2: 7 + x = 12 Variable A symbol, usually a letter, that is used to represent one or more
More informationMath 8 Honors Coordinate Geometry part 1 Unit Updated July 29, 2016
Reviewing the basics The number line A number line is a visual representation of all real numbers. Each of the images below are examples of number lines. The top left one includes only positive whole numbers,
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 informationMathematics Diagnostic Examination Guidance
Mathematics Diagnostic Examination Guidance Examination Overview The mathematics examination will be 45 minutes long and will be worth 50 points. There will be three sections on the examination: Section
More informationHere are the exams I wrote when teaching Math 115 in Fall 2018 at Ferris State University. Each exam is followed by its solutions.
Here are the exams I wrote when teaching Math 5 in Fall 208 at Ferris State University. Each exam is followed by its solutions. Fall 208 Exam. (a) Find the slope of the line passing through the points
More information1.2 Graphs and Lines. Cartesian Coordinate System
1.2 Graphs and Lines Cartesian Coordinate System Note that there is a one-to-one correspondence between the points in a plane and the elements in the set of all ordered pairs (a, b) of real numbers. Graphs
More informationLesson 26: Characterization of Parallel Lines
Student Outcomes Students know that when a system of linear equations has no solution, i.e., no point of intersection of the lines, then the lines are parallel. Lesson Notes The discussion that begins
More informationChapter P. Prerequisites. Slide P- 1. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide P- 1 Chapter P Prerequisites 1 P.1 Real Numbers Quick Review 1. List the positive integers between -4 and 4.. List all negative integers greater than -4. 3. Use a calculator to evaluate the expression
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A) 5 B) 277 C) 126 D) 115
MAC 1 Sullivan Practice for Chapter 2 Test (Kincade) Name Date Section MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(p1, P2)
More information8.3 GRAPH AND WRITE EQUATIONS OF CIRCLES
8.3 GRAPH AND WRITE EQUATIONS OF CIRCLES What is the standard form equation for a circle? Why do you use the distance formula when writing the equation of a circle? What general equation of a circle is
More informationGUIDED NOTES 4.1 LINEAR FUNCTIONS
GUIDED NOTES 4.1 LINEAR FUNCTIONS LEARNING OBJECTIVES In this section, you will: Represent a linear function. Determine whether a linear function is increasing, decreasing, or constant. Interpret slope
More informationMath 1 packet for Coordinate Geometry part 1. Reviewing the basics. The coordinate plane
Math 1 packet for Coordinate Geometry part 1 Reviewing the basics The coordinate plane The coordinate plane (also called the Cartesian plane named after French mathematician Rene Descartes, who formalized
More informationSample Final Exam. Math S o l u t i o n s. 1. Three points are given: A = ( 2, 2), B = (2, 4), C = ( 4, 0)
Math 0031 Sample Final Exam S o l u t i o n s 1. Three points are given: A = ( 2, 2), B = (2, 4), C = ( 4, 0) (a) (5 points) Find the midpoint D of the segment with endpoints B and C. ( 2 + ( 4) D =, 4
More informationChapter 2: Inequalities, Functions, and Linear Functions
CHAPTER Chapter : Inequalities, Functions, and Linear Functions Exercise.. a. + ; ; > b. ; + ; c. + ; ; > d. 7 ; 8 ; 8 < e. 0. 0. 0.; 0. 0. 0.6; 0. < 0.6 f....0;. (0.).0;.0 >.0 Inequality Line Graph Inequality
More informationBasic Fraction and Integer Operations (No calculators please!)
P1 Summer Math Review Packet For Students entering Geometry The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Geometry.
More informationChapter 3. Graphing Linear Equations and Functions
Chapter 3 Graphing Linear Equations and Functions 3.1 Plot Points in a Coordinate Plane Coordinate Plane- Two intersecting at a angle. x-axis the axis y-axis the axis The coordinate plane is divided into.
More informationSKILL BUILDER TEN. Graphs of Linear Equations with Two Variables. If x = 2 then y = = = 7 and (2, 7) is a solution.
SKILL BUILDER TEN Graphs of Linear Equations with Two Variables A first degree equation is called a linear equation, since its graph is a straight line. In a linear equation, each term is a constant or
More informationExample 2.1. Draw the points with polar coordinates: (i) (3, π) (ii) (2, π/4) (iii) (6, 2π/4) We illustrate all on the following graph:
Section 10.3: Polar Coordinates The polar coordinate system is another way to coordinatize the Cartesian plane. It is particularly useful when examining regions which are circular. 1. Cartesian Coordinates
More informationLinear vs. Exponential Word Problems
Linear vs. Eponential Word Problems At separate times in the course, you ve learned about linear functions and eponential functions, and done word problems involving each type of function. Today s assignment
More informationSample Questions to the Final Exam in Math 1111 Chapter 2 Section 2.1: Basics of Functions and Their Graphs
Sample Questions to the Final Eam in Math 1111 Chapter Section.1: Basics of Functions and Their Graphs 1. Find the range of the function: y 16. a.[-4,4] b.(, 4],[4, ) c.[0, ) d.(, ) e.. Find the domain
More informationALGEBRA 2 Summer Review Assignments Graphing
ALGEBRA 2 Summer Review Assignments Graphing To be prepared for algebra two, and all subsequent math courses, you need to be able to accurately and efficiently find the slope of any line, be able to write
More informationAlgebra I EOC Review (Part 2)
1. Let x = total miles the car can travel Answer: x 22 = 18 or x 18 = 22 2. A = 1 2 ah 1 2 bh A = 1 h(a b) 2 2A = h(a b) 2A = h a b Note that when solving for a variable that appears more than once, consider
More informationGraphing and Writing Linear Equations Review 3.1, 3.3, & 4.4. Name: Date: Period:
Graphing and Writing Linear Equations Review.1,., 4.1-4. & 4.4 Algebra I Name: Date: Period: Quest Topics Section.1 linear versus nonlinear rewrite linear equations in standard form: Ax By C find and use
More informationAlong the way, you learned many manipulative skills using the Properties of Real Numbers.
A LOOK at Algebra ============================= In a nutshell, you have learned how to: 1. solve linear equations and inequalities. solve quadratic equations and inequalities 3. solve systems of linear
More informationMath 1010 Lesson 1-4 (Textbook 1.7 and 1.8) Different equations of Lines
Math 00 Lesson -4 (Textbook.7 and.8) Different equations of Lines. slope intercept form = mx + b. standard form Ax + B = C m x x 3. point slope form ( ) Which one we use depends on what information is
More informationLHS Algebra Pre-Test
Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well
More informationAccuplacer Elementary Algebra Review
Accuplacer Elementary Algebra Review Hennepin Technical College Placement Testing for Success Page 1 Overview The Elementary Algebra section of ACCUPLACER contains 1 multiple choice Algebra questions that
More informationMath Precalculus I University of Hawai i at Mānoa Spring
Math 135 - Precalculus I University of Hawai i at Mānoa Spring - 2013 Created for Math 135, Spring 2008 by Lukasz Grabarek and Michael Joyce Send comments and corrections to lukasz@math.hawaii.edu Contents
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
ALGEBRA 1 Standard 1 Operations with Real Numbers Students simplify and compare expressions. They use rational exponents, and simplify square roots. A1.1.1 A1.1.2 A1.1.3 A1.1.4 A1.1.5 Compare real number
More information1.3 Linear Functions
1.3 Linear Functions A function of the form f(x) = ax + b, where a and b are constants, is called a linear function. The graph of f(x) = ax + b or y = mx + b, is a line, with slope a (or m), and y intercept
More informationDuVal High School Summer Review Packet AP Calculus
DuVal High School Summer Review Packet AP Calculus Welcome to AP Calculus AB. This packet contains background skills you need to know for your AP Calculus. My suggestion is, you read the information and
More informationALGEBRA 2 SUMMER WORK. June Dear Algebra 2 Students,
ALGEBRA SUMMER WORK June 016 Dear Algebra Students, Below you will find the Summer Math Packet for Algebra. The purpose of this packet is to review and sharpen your Algebra 1 skills so that when we return
More informationHow can we see it? Is there another way?
You have solved a variety of equations in this course. In this lesson, by looking at equations in different ways, you will be able to solve even more complicated equations quickly and easily. These new
More informationElementary Algebra SAMPLE Final Examination Spring 2015
Elementary Algebra NAME: SAMPLE Final Examination Spring 2015 You will have 2 hours to complete this exam. You may use a calculator but must show all algebraic work in the space provided to receive full
More informationName: Class: Date: Unit 1. Thinking with Mathematical Models Investigation 2: Linear Models & Equations. Practice Problems
Unit 1 Thinking with Mathematical Models Investigation 2: Linear Models & Equations Practice Problems Directions: Please complete the necessary problems to earn a maximum of 7 points according to the chart
More informationNAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve = 6 3v = -3(c + 5)
FINAL EXAM REVIEW, p. 1 NAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve. 1. = 6 v. 1 = -(c + 5). 5 (x ) = 6. 7x + = 5x + 8 5. r 1 1 6. x 1 x 5 Write an equation, and then solve. 7. Ben joined The
More informationLesson 3 - Linear Functions
Lesson 3 - Linear Functions Introduction As an overview for the course, in Lesson's 1 and 2 we discussed the importance of functions to represent relationships and the associated notation of these functions
More informationLesson Mathematical Linear Models
STATWAY STUDENT HANDOUT STUDENT NAME DATE INTRODUCTION Jean needs to buy some meat for her housing co-operative. She can go to the Fresh-Plus store to buy it for $3.50 per pound. Or she can go to the warehouse
More informationCP Algebra 2. Summer Packet. Name:
CP Algebra Summer Packet 018 Name: Objectives for CP Algebra Summer Packet 018 I. Number Sense and Numerical Operations (Problems: 1 to 4) Use the Order of Operations to evaluate expressions. (p. 6) Evaluate
More informationAlgebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher
Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work
More informationSummer Packet for Students Taking Introduction to Calculus in the Fall
Summer Packet for Students Taking Introduction to Calculus in the Fall Algebra 2 Topics Needed for Introduction to Calculus Need to know: à Solve Equations Linear Quadratic Absolute Value Polynomial Rational
More informationHorizontal and Vertical Lines
Horizontal and Vertical Lines 1 9. Calculate the slope of the line pictured below 10. Calculate the slope of the line pictured below Conclusions: Horizontal Lines Vertical Lines http://www.mathsisfun.com/flash.php?path=%2falgebra/images/line-toequation.swf&w=600&h=600&col=%23ffffff&title=equation+of+a+line+from+2+points
More informationALGEBRA MIDTERM REVIEW SHEET
Name Date Part 1 (Multiple Choice): Please show ALL work! ALGEBRA MIDTERM REVIEW SHEET 1) The equations 5x 2y 48 and 3x 2y 32 represent the money collected from school concert ticket sales during two class
More informationKing Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 181 Recitation (1.1)
Recitation (1.1) Question 1: Find a point on the y-axis that is equidistant from the points (5, 5) and (1, 1) Question 2: Find the distance between the points P(2 x, 7 x) and Q( 2 x, 4 x) where x 0. Question
More informationSections 8.1 & 8.2 Systems of Linear Equations in Two Variables
Sections 8.1 & 8.2 Systems of Linear Equations in Two Variables Department of Mathematics Porterville College September 7, 2014 Systems of Linear Equations in Two Variables Learning Objectives: Solve Systems
More informationStudent Instruction Sheet: Unit 2, Lesson 2. Equations of Lines, Part 2
Student Instruction Sheet: Unit 2, Lesson 2 Suggested Time: 50 minutes What s important in this lesson: Equations of Lines, Part 2 In this lesson, you will learn how to write equations of lines, given
More informationAlgebra One Dictionary
Algebra One Dictionary Page 1 of 17 A Absolute Value - the distance between the number and 0 on a number line Algebraic Expression - An expression that contains numbers, operations and at least one variable.
More informationCOMMON CORE MATHEMATICS CURRICULUM
COMMON CORE MATHEMATICS CURRICULUM Lesson 1 8 4 Lesson 1: Writing Equations Using Symbols Write each of the following statements using symbolic language. 1. When you square five times a number you get
More informationSection 3.4 Writing the Equation of a Line
Chapter Linear Equations and Functions Section.4 Writing the Equation of a Line Writing Equations of Lines Critical to a thorough understanding of linear equations and functions is the ability to write
More informationAP Calculus I Summer Packet
AP Calculus I Summer Packet This will be your first grade of AP Calculus and due on the first day of class. Please turn in ALL of your work and the attached completed answer sheet. I. Intercepts The -intercept
More informationFOR ALL STUDENTS TAKING ALGEBRA II Honors SUMMER REVIEW PACKET
FOR ALL STUDENTS TAKING ALGEBRA II Honors 01-014 SUMMER REVIEW PACKET Dear Student and Parent/Guardian, The math department at Central Dauphin School District wants you to be successful in Algebra II.
More informationNOTES. [Type the document subtitle] Math 0310
NOTES [Type the document subtitle] Math 010 Cartesian Coordinate System We use a rectangular coordinate system to help us map out relations. The coordinate grid has a horizontal axis and a vertical axis.
More information(c) log 1 4 (d) log 3 3. Use logarithm properties for expanding to rewrite the expression in
AP Calculus AB Summer Assignment for 2017-2018 School Year Mrs. Brennan In order to be prepared for next year and be ready to move on to new work, you must have skills required to do these problems with
More informationRate of Change and slope. Objective: To find rates of change from tables. To find slope.
Linear Functions Rate of Change and slope Objective: To find rates of change from tables. To find slope. Objectives I can find the rate of change using a table. I can find the slope of an equation using
More informationPrecalculus Summer Packet
Precalculus Summer Packet These problems are to be completed to the best of your ability by the first day of school You will be given the opportunity to ask questions about problems you found difficult
More informationMath 2 Variable Manipulation Part 7 Absolute Value & Inequalities
Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,
More informationGOOD LUCK! 2. a b c d e 12. a b c d e. 3. a b c d e 13. a b c d e. 4. a b c d e 14. a b c d e. 5. a b c d e 15. a b c d e. 6. a b c d e 16.
MA109 College Algebra Fall 2018 Practice Final Exam 2018-12-12 Name: Sec.: Do not remove this answer page you will turn in the entire exam. You have two hours to do this exam. No books or notes may be
More informationRecognise the Equation of a Circle. Solve Problems about Circles Centred at O. Co-Ordinate Geometry of the Circle - Outcomes
1 Co-Ordinate Geometry of the Circle - Outcomes Recognise the equation of a circle. Solve problems about circles centred at the origin. Solve problems about circles not centred at the origin. Determine
More information