Grade 10 Applied Math Unit 3: Linear Equations Lesson: Date: Completed Level Lesson 1: Coordinates Review Lesson 2: Constructing Tables and Sketching

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Grade 10 Applied Math Unit 3: Linear Equations Lesson: Date: Completed Level Lesson 1: Coordinates Review Lesson 2: Constructing Tables and Sketching"

Transcription

1 Grade 10 Applied Math Unit 3: Linear Equations Lesson: Date: Completed Level Lesson 1: Coordinates Review Lesson 2: Constructing Tables and Sketching Graphs Lesson 3: Interpreting Lines Lesson 4: Write Linear Equations by Using a Table of Values Lesson 5: Write Linear Equations by Translating Written Descriptions Lesson 6: Reviewing Key Concepts Reminiscing Old Relationship Key Concepts Lesson 7: More Initial Value and Slope Variables and Equations with Graphs Lesson 7: More Initial Value and Slope Slopes and Stuff Homework Lesson 7: More Initial Value and Slope Graphs, Slopes, Intercepts and Equations Check Lesson 8: Graphing from an Equation Can Graphing Get Any Easier? Lesson 8: Graphing from an Equation Rising and Running From a Point? Lesson 9: Conversions Temperature Conversions Lesson 9: Conversions Temperature Conversions - Practice Lesson 9: Conversions Modelling Algebraically Problems Lesson 9: Conversions Practice Models Lesson 10: Finding x and y intercepts Y and X Are you Intercepting Me? Lesson 10: Finding x and y intercepts Y and X Are you Intercepting Me Practice Lesson 10: Finding x and y intercepts Writing Equations of Lines Lesson 10: Finding x and y intercepts Jack and Jill Go up a Hill Lesson 10: Finding x and y intercepts Slopes A way Lesson 11: Writing Equations 3.8.4: Writing Equations of Lines Lesson 12: Writing Equations without Graphing 3.9.2: Yes, We got no Graph Paper! Lesson 13: Converting from Standard Form to Slope Y-intercept form Practice Problems Lesson 13: Converting from Standard Form to Slope Y-intercept form Converting from Standard to Slope Y-Intercept Form - Practice Lesson 14: Review Unit 3 Test

2 Unit 3: Lesson 1 - Coordinates Review

3

4

5

6 Unit 3: Lesson 2 - Constructing Tables and Sketching Graphs Practice Problems Level 1: 1. For each table of values, find the missing values. a) b) c) d) 2. Complete each table of values. 3. Find two other points that would fit on the lines below. a) b)

7 Level 2: 4. Determine if the point satisfies the equation of the line. a) A(2, 1); y = 2x 5 b) B(3, 1); y = x + 2 c) C( 4, 3); y = 3x + 4 d) D( 2, 2); y = 4x A telephone carrier offers phone calls for 9 /min to Scotland. a) Write an equation relating the cost, c (in dollars), to the time, t (in minutes). b) Develop a table of values for each minute up to 8 min of phone calls to Scotland. c) Graph the relation on a Cartesian plane

8 Level 3: 6. A hardware store offers its customers 5 in coupons for every dollar spent in its store. The equation relating money spent, m (in dollars), to value of coupons, c(in dollars), is c=0.05m a) Develop a table up to $100 in purchases for the b) Graph the results of your table hardware store. Use m-values of 0, 25, 50, 75, 100. c) Explain how the value of coupons received for $0, $75, and $100 compares to the value of coupons received for $25 d) Use your graph or table of values to determine the value of the coupons that you would receive for $175 in purchases.

9 Level 4: 7. Paramount Canada s Wonderland offers group discounted pricing as shown in the table. A group consists of a minimum of 25 people. The total group cost, c (in dollars), is found by multiplying the season price by the number of people, p, in the group. a) Write an equation to represent the total group cost for each season priced ticket. Then develop tables of values for all three seasons. Use a minimum of five p-values for each table. b) Graph the 3 lines on the same set of axes. c) How much money would a group of 25 people save by choosing to go to Paramount Canada s Wonderland during the fall instead of the summer?

10 Unit 3: Lesson 3 - Interpreting Lines Practice Problems Level 1: 1. Use points A and B to determine the slope in each diagram. 2. Find the slope of the line that passes through each pair of points. a) (4, 5) and (8, 11) b) ( 3, 4) and ( 5, 6) 3. State the slope and y-intercept for each linear equation. a) y = 3x + 4 b) y = 2x 3 c) + 1 d) y = 0.5x 2

11 Level 2: 4. Determine the slope of the roof. 5. The graph shows the increase in the price of admission over a 4-year period. Change the scales on the axes in two different ways. Describe how the increase in the price of admission appears in each of your graphs. Level 3: 6. For safety reasons, it is recommended that a wheelchair ramp be built with a 1 m rise and a 12 m run. a) What is the slope of the ramp? b) If the rise is only 65 cm, what will the run be using the slope from part a)? 7. If a hill has a grade of 6%, this means that for every 100m of horizontal change, there is a vertical change of 6m. If a road has a 6% grade, what is the vertical change, in metres, when the horizontal change is 4km?

12 Unit 3: Lesson 4 - Write Linear Equations by using a table of values Practice Problems Level 1: 1. Determine the slope and y-intercept for the graph of each line. a) b) 2. Find an equation in the form y = mx + b for the straight line represented by each table of values. a) b) 3. Determine the equation of a line given its slope, m, and y-intercept, b. a) m = 3, b = 4 b) m = 2, b = 3 c) m = 5, b = 6 d)

13 Level 2: 4. Graph the line represented by each table. Label the line with its equation. a) b) For the ramp below, write an equation in the form y = mx + b. Level 3: 6. BZB Parking charges $3.00 for 1 h of parking, $4.50 for 1.5 h of parking, and $6.00 for 2 h of parking. a) Write an equation that represents this relationship. Define your variables. b) What do the slope and y-intercept represent? c) Use the equation from part a) to predict the cost of 4 h of parking.

14 7. At Super Suds Car Wash 4 minutes of service will cost $2.00, 7 min cost $3.50, and ten minutes cost $5.00. a) Write an equation that represents this relationship. Define your variables. b) What is the cost per minute? c) What is the y-intercept? Explain what this means? Level 4: 8. Carpets-R-Us charges a standard fee plus an hourly rate for every job they are contracted to do. They charge $60 for a 1-h job, $100 for a 2-h job, and $140 for a 3-h job. a) Write an equation that represents this relationship. Define your variables. b) What doe the slope and y-intercept represent? c) Use the equation from part a) to predict the charge for a 5-h job.

15 9. a) Find an equation for the straight line represented in each table of values. Comment on the relationship between the slopes of the lines. x x y y b) Graph both lines on the same set of axes. c) What is the geometric relationship between the graphs of these lines? d) Write a pair of equations whose graphs have this same relationship.

What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.

What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b. PRIMARY CONTENT MODULE Algebra - Linear Equations & Inequalities T-37/H-37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of

More information

GRAPHING LINEAR EQUATIONS IN TWO VARIABLES

GRAPHING LINEAR EQUATIONS IN TWO VARIABLES GRAPHING LINEAR EQUATIONS IN TWO VARIABLES The graphs of linear equations in two variables are straight lines. Linear equations may be written in several forms: Slope-Intercept Form: y = mx+ b In an equation

More information

Solving Equations Involving Parallel and Perpendicular Lines Examples

Solving Equations Involving Parallel and Perpendicular Lines Examples Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines

More information

Pre-AP Algebra 2 Lesson 2-5 Graphing linear inequalities & systems of inequalities

Pre-AP Algebra 2 Lesson 2-5 Graphing linear inequalities & systems of inequalities Lesson 2-5 Graphing linear inequalities & systems of inequalities Objectives: The students will be able to - graph linear functions in slope-intercept and standard form, as well as vertical and horizontal

More information

1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved.

1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved. 1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points

More information

The Point-Slope Form

The Point-Slope Form 7. The Point-Slope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope

More information

Slope-Intercept Equation. Example

Slope-Intercept Equation. Example 1.4 Equations of Lines and Modeling Find the slope and the y intercept of a line given the equation y = mx + b, or f(x) = mx + b. Graph a linear equation using the slope and the y-intercept. Determine

More information

MiSP Simple Machines/Inclined Plane Worksheet #2b L3 Modified from Making the Grade (AIMS Machine Shop)

MiSP Simple Machines/Inclined Plane Worksheet #2b L3 Modified from Making the Grade (AIMS Machine Shop) MiSP Simple Machines/Inclined Plane Worksheet #2b L3 Modified from Making the Grade (AIMS Machine Shop) Name Date L 1, 2, 3 Key Question: How much force does it take to lift 400 grams 20 centimeters in

More information

Section 1.4 Notes Page Linear Equations in Two Variables and Linear Functions., x

Section 1.4 Notes Page Linear Equations in Two Variables and Linear Functions., x Section. Notes Page. Linear Equations in Two Variables and Linear Functions Slope Formula The slope formula is used to find the slope between two points ( x, y ) and ( ) x, y. x, y ) The slope is the vertical

More information

Number of Solutions to Simultaneous Equations

Number of Solutions to Simultaneous Equations Worksheet 3.5 Simultaneous Equations Section 1 Number of Solutions to Simultaneous Equations In maths we are sometimes confronted with two equations in two variables and we want to find out which values

More information

In this section, we ll review plotting points, slope of a line and different forms of an equation of a line.

In this section, we ll review plotting points, slope of a line and different forms of an equation of a line. Math 1313 Section 1.2: Straight Lines In this section, we ll review plotting points, slope of a line and different forms of an equation of a line. Graphing Points and Regions Here s the coordinate plane:

More information

Writing the Equation of a Line in Slope-Intercept Form

Writing the Equation of a Line in Slope-Intercept Form Writing the Equation of a Line in Slope-Intercept Form Slope-Intercept Form y = mx + b Example 1: Give the equation of the line in slope-intercept form a. With y-intercept (0, 2) and slope -9 b. Passing

More information

MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

More information

A synonym is a word that has the same or almost the same definition of

A synonym is a word that has the same or almost the same definition of Slope-Intercept Form Determining the Rate of Change and y-intercept Learning Goals In this lesson, you will: Graph lines using the slope and y-intercept. Calculate the y-intercept of a line when given

More information

WARM UP EXERCSE. 1-3 Linear Functions & Straight lines

WARM UP EXERCSE. 1-3 Linear Functions & Straight lines WARM UP EXERCSE A company makes and sells inline skates. The price-demand function is p (x) = 190 0.013(x 10) 2. Describe how the graph of function p can be obtained from one of the library functions.

More information

4.4 scatterplots and lines of fit2 ink.notebook. November 29, Standards. Scatter Plot. negative correlation. positive correlation

4.4 scatterplots and lines of fit2 ink.notebook. November 29, Standards. Scatter Plot. negative correlation. positive correlation . scatterplots and lines of fit ink.notebook Page 7 Page 7. Scatter Plots and Line of Fit Page 7 Page 7 Page 7 Page 76 . scatterplots and lines of fit ink.notebook Lesson Objectives Standards Lesson Notes

More information

Equations of Lines Derivations

Equations of Lines Derivations Equations of Lines Derivations If you know how slope is defined mathematically, then deriving equations of lines is relatively simple. We will start off with the equation for slope, normally designated

More information

Answer on Question #48173 Math Algebra

Answer on Question #48173 Math Algebra Answer on Question #48173 Math Algebra On graph paper, draw the axes, and the lines y = 12 and x = 6. The rectangle bounded by the axes and these two lines is a pool table with pockets in the four corners.

More information

Ordered Pairs. Graphing Lines and Linear Inequalities, Solving System of Linear Equations. Cartesian Coordinates System.

Ordered Pairs. Graphing Lines and Linear Inequalities, Solving System of Linear Equations. Cartesian Coordinates System. Ordered Pairs Graphing Lines and Linear Inequalities, Solving System of Linear Equations Peter Lo All equations in two variables, such as y = mx + c, is satisfied only if we find a value of x and a value

More information

Graphing Linear Equations

Graphing Linear Equations Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope

More information

Sect The Slope-Intercept Form

Sect The Slope-Intercept Form 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 information

Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year.

Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year. Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year. Goal The goal of the summer math program is to help students

More information

Lesson 22: Solution Sets to Simultaneous Equations

Lesson 22: Solution Sets to Simultaneous Equations Student Outcomes Students identify solutions to simultaneous equations or inequalities; they solve systems of linear equations and inequalities either algebraically or graphically. Classwork Opening Exercise

More information

Section 3.2. Graphing linear equations

Section 3.2. Graphing linear equations Section 3.2 Graphing linear equations Learning objectives Graph a linear equation by finding and plotting ordered pair solutions Graph a linear equation and use the equation to make predictions Vocabulary:

More information

Chapter 8 Graphs and Functions:

Chapter 8 Graphs and Functions: Chapter 8 Graphs and Functions: Cartesian axes, coordinates and points 8.1 Pictorially we plot points and graphs in a plane (flat space) using a set of Cartesian axes traditionally called the x and y axes

More information

5 $75 6 $90 7 $105. Name Hour. Review Slope & Equations of Lines. STANDARD FORM: Ax + By = C. 1. What is the slope of a vertical line?

5 $75 6 $90 7 $105. Name Hour. Review Slope & Equations of Lines. STANDARD FORM: Ax + By = C. 1. What is the slope of a vertical line? Review Slope & Equations of Lines Name Hour STANDARD FORM: Ax + By = C 1. What is the slope of a vertical line? 2. What is the slope of a horizontal line? 3. Is y = 4 the equation of a horizontal or vertical

More information

GRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points?

GRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points? GRAPHING (2 weeks) The Rectangular Coordinate System 1. Plot ordered pairs of numbers on the rectangular coordinate system 2. Graph paired data to create a scatter diagram 1. How do you graph points? 2.

More information

Linear Equations and Graphs

Linear Equations and Graphs 2.1-2.4 Linear Equations and Graphs Coordinate Plane Quadrants - The x-axis and y-axis form 4 "areas" known as quadrants. 1. I - The first quadrant has positive x and positive y points. 2. II - The second

More information

EQUATIONS and INEQUALITIES

EQUATIONS and INEQUALITIES EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line

More information

MATH 105: Finite Mathematics 1-1: Rectangular Coordinates, Lines

MATH 105: Finite Mathematics 1-1: Rectangular Coordinates, Lines MATH 105: Finite Mathematics 1-1: Rectangular Coordinates, Lines Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline 1 Rectangular Coordinate System 2 Graphing Lines 3 The Equation of

More information

Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan

Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan I. Topic: Slope-Intercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.

More information

COMPARING LINEAR AND NONLINEAR FUNCTIONS

COMPARING LINEAR AND NONLINEAR FUNCTIONS 1 COMPARING LINEAR AND NONLINEAR FUNCTIONS LEARNING MAP INFORMATION STANDARDS 8.F.2 Compare two s, each in a way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example,

More information

Unit 5: Coordinate Geometry Practice Test

Unit 5: Coordinate Geometry Practice Test Unit 5: Coordinate Geometry Practice Test Math 10 Common Name: Block: Please initial this box to indicate you carefully read over your test and checked your work for simple mistakes. What I can do in this

More information

Helpsheet. Giblin Eunson Library LINEAR EQUATIONS. library.unimelb.edu.au/libraries/bee. Use this sheet to help you:

Helpsheet. Giblin Eunson Library LINEAR EQUATIONS. library.unimelb.edu.au/libraries/bee. Use this sheet to help you: Helpsheet Giblin Eunson Library LINEAR EQUATIONS Use this sheet to help you: Solve linear equations containing one unknown Recognize a linear function, and identify its slope and intercept parameters Recognize

More information

Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}

Linear 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 information

Slope-Intercept Form of a Linear Equation Examples

Slope-Intercept Form of a Linear Equation Examples Slope-Intercept Form of a Linear Equation Examples. In the figure at the right, AB passes through points A(0, b) and B(x, y). Notice that b is the y-intercept of AB. Suppose you want to find an equation

More information

Write the Equation of the Line Review

Write the Equation of the Line Review Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Objective: Students will be assessed on their ability to write the equation of a line in multiple methods. Connections

More information

Final Graphing Practice #1

Final Graphing Practice #1 Final Graphing Practice #1 Beginning Algebra / Math 100 Fall 2013 506 (Prof. Miller) Student Name/ID: Instructor Note: Assignment: Set up a tutoring appointment with one of the campus tutors or with me.

More information

Section 3.4 The Slope Intercept Form: y = mx + b

Section 3.4 The Slope Intercept Form: y = mx + b Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept Reminding! m = y x = y 2 y 1 x 2 x 1 Slope of a horizontal line is 0 Slope of a vertical line is Undefined Graph a linear

More information

Linear Equations Review

Linear Equations Review Linear Equations Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The y-intercept of the line y = 4x 7 is a. 7 c. 4 b. 4 d. 7 2. What is the y-intercept

More information

Beginning of the Semester To-Do List

Beginning of the Semester To-Do List Beginning of the Semester To-Do List Set up your account at https://casa.uh.edu/ Read the Math 13xx Departmental Course Policies Take Course Policies Quiz until your score is 100%. You can find it on the

More information

The slope m of the line passes through the points (x 1,y 1 ) and (x 2,y 2 ) e) (1, 3) and (4, 6) = 1 2. f) (3, 6) and (1, 6) m= 6 6

The slope m of the line passes through the points (x 1,y 1 ) and (x 2,y 2 ) e) (1, 3) and (4, 6) = 1 2. f) (3, 6) and (1, 6) m= 6 6 Lines and Linear Equations Slopes Consider walking on a line from left to right. The slope of a line is a measure of its steepness. A positive slope rises and a negative slope falls. A slope of zero means

More information

Lines and Linear Equations. Slopes

Lines and Linear Equations. Slopes Lines and Linear Equations Slopes Consider walking on a line from left to right. The slope of a line is a measure of its steepness. A positive slope rises and a negative slope falls. A slope of zero means

More information

) represents the original function, will a, r 1

) represents the original function, will a, r 1 Transformations of Quadratic Functions Focus on Content: Download Problem Sets Problem Set #1 1. In the graph below, the quadratic function displayed on the right has been reflected over the y-axis producing

More information

Functions in Standard Form

Functions in Standard Form 2-2 Properties of of Quadratic Functions in Functions in Warm Up Lesson Presentation Lesson Quiz Algebra 2 2-1 Using Transformations to Graph Quadratic Functions Warm Up For each translation of the point

More information

5.1: Rate of Change and Slope

5.1: Rate of Change and Slope 5.1: Rate of Change and Slope Rate of Change shows relationship between changing quantities. On a graph, when we compare rise and run, we are talking about steepness of a line (slope). You can use and

More information

Many different kinds of animals can change their form to help them avoid or

Many different kinds of animals can change their form to help them avoid or Slopes, Forms, Graphs, and Intercepts Connecting the Standard Form with the Slope-Intercept Form of Linear Functions Learning Goals In this lesson, you will: Graph linear functions in standard form. Transform

More information

Lecture 9: Lines. m = y 2 y 1 x 2 x 1

Lecture 9: Lines. m = y 2 y 1 x 2 x 1 Lecture 9: Lines If we have two distinct points in the Cartesian plane, there is a unique line which passes through the two points. We can construct it by joining the points with a straight edge and extending

More information

Section 1.1 Linear Equations: Slope and Equations of Lines

Section 1.1 Linear Equations: Slope and Equations of Lines Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of

More information

Pre-AP Algebra 2 Unit 3 Lesson 1 Quadratic Functions

Pre-AP Algebra 2 Unit 3 Lesson 1 Quadratic Functions Unit 3 Lesson 1 Quadratic Functions Objectives: The students will be able to Identify and sketch the quadratic parent function Identify characteristics including vertex, axis of symmetry, x-intercept,

More information

Math 152 Rodriguez Blitzer 2.4 Linear Functions and Slope

Math 152 Rodriguez Blitzer 2.4 Linear Functions and Slope Math 152 Rodriguez Blitzer 2.4 Linear Functions and Slope I. Linear Functions 1. A linear equation is an equation whose graph is a straight line. 2. A linear equation in standard form: Ax +By=C ex: 4x

More information

Section 2.2 Equations of Lines

Section 2.2 Equations of Lines Section 2.2 Equations of Lines The Slope of a Line EXAMPLE: Find the slope of the line that passes through the points P(2,1) and Q(8,5). = 5 1 8 2 = 4 6 = 2 1 EXAMPLE: Find the slope of the line that passes

More information

Lines That Pass Through Regions

Lines That Pass Through Regions : Student Outcomes Given two points in the coordinate plane and a rectangular or triangular region, students determine whether the line through those points meets the region, and if it does, they describe

More information

Algebra I. In this technological age, mathematics is more important than ever. When students

Algebra I. In this technological age, mathematics is more important than ever. When students In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,

More information

Quadratic Functions and Models

Quadratic Functions and Models Quadratic Functions and Models MATH 160, Precalculus J. Robert Buchanan Department of Mathematics Fall 2011 Objectives In this lesson we will learn to: analyze the graphs of quadratic functions, write

More information

Use the graph shown to determine whether each system is consistent or inconsistent and if it is independent or dependent.

Use the graph shown to determine whether each system is consistent or inconsistent and if it is independent or dependent. Use the graph shown to determine whether each system is consistent or inconsistent and if it is independent or dependent. y = 3x + 1 y = 3x + 1 The two equations intersect at exactly one point, so they

More information

ModuMath Algebra Lessons

ModuMath Algebra Lessons ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations

More information

Unit 4. Linear Functions OUTLINE

Unit 4. Linear Functions OUTLINE Unit 4 Linear Functions This unit formalizes vocabulary and processes involved in finding and analyzing attributes of linear functions. The strategies and routines that you have been developing will enhance

More information

The Cartesian Plane The Cartesian Plane. Performance Criteria 3. Pre-Test 5. Coordinates 7. Graphs of linear functions 9. The gradient of a line 13

The Cartesian Plane The Cartesian Plane. Performance Criteria 3. Pre-Test 5. Coordinates 7. Graphs of linear functions 9. The gradient of a line 13 6 The Cartesian Plane The Cartesian Plane Performance Criteria 3 Pre-Test 5 Coordinates 7 Graphs of linear functions 9 The gradient of a line 13 Linear equations 19 Empirical Data 24 Lines of best fit

More information

Algebra I: Strand 1. Foundations of Functions; Topic 3. Changing Perimeter; Task 1.3.1

Algebra I: Strand 1. Foundations of Functions; Topic 3. Changing Perimeter; Task 1.3.1 1 TASK 1.3.1: CHANGING PERIMETER TEACHER ACTIVITY Solutions On a sheet of grid paper create one set of axes. Label the axes for this situation perimeter vs. multiplier. Graph your prediction data for changing

More information

1-7 Inverse Relations and Functions

1-7 Inverse Relations and Functions Graph each function using a graphing calculator, and apply the horizontal line test to determine whether its inverse function exists. Write yes or no. 3. f (x) = x 10x + 5 1. f (x) = x + 6x + 9 The graph

More information

Name: Class: Date: Does the equation represent a direct variation? If so, find the constant of variation. c. yes; k = 5 3. c.

Name: Class: Date: Does the equation represent a direct variation? If so, find the constant of variation. c. yes; k = 5 3. c. Name: Class: Date: Chapter 5 Test Multiple Choice Identify the choice that best completes the statement or answers the question. What is the slope of the line that passes through the pair of points? 1.

More information

TEACHER NOTES MATH NSPIRED

TEACHER NOTES MATH NSPIRED Math Objectives Students will use a moveable line to find a line of fit for a data set. Students will interpret the slope and y-intercept of the equation of their line of fit. Students will make predictions

More information

Lesson 8.3 Exercises, pages

Lesson 8.3 Exercises, pages Lesson 8. Eercises, pages 57 5 A. For each function, write the equation of the corresponding reciprocal function. a) = 5 - b) = 5 c) = - d) =. Sketch broken lines to represent the vertical and horizontal

More information

Lesson Plan Mine Shaft Grade 8 Slope

Lesson Plan Mine Shaft Grade 8 Slope CCSSM: Grade 8 DOMAIN: Expressions and Equations Cluster: Understand the connections between proportional relationships, lines, and linear equations. Standard: 8.EE.5: Graph proportional relationships,

More information

DO NOW Geometry Regents Lomac Date. due. Coordinate Plane: Equation of a Circle

DO NOW Geometry Regents Lomac Date. due. Coordinate Plane: Equation of a Circle DO NOW Geometry Regents Lomac 2014-2015 Date. due. Coordinate Plane: Equation of a Circle 8.5 (DN) TEAR OFF The Circle PAGE AND THEN DO THE DO NOW ON BACK OF PACKET (1) What do right triangles have to

More information

Aim: How do we find the slope of a line? Warm Up: Go over test. A. Slope -

Aim: How do we find the slope of a line? Warm Up: Go over test. A. Slope - Aim: How do we find the slope of a line? Warm Up: Go over test A. Slope - Plot the points and draw a line through the given points. Find the slope of the line.. A(-5,4) and B(4,-3) 2. A(4,3) and B(4,-6)

More information

Algebra II. American Heritage Upper School Summer Math Packet

Algebra II. American Heritage Upper School Summer Math Packet American Heritage Upper School Summer Math Packet All Upper School American Heritage math students are required to complete a summer math packet. This packet is intended for all students entering Algebra

More information

Section 1.4 Graphs of Linear Inequalities

Section 1.4 Graphs of Linear Inequalities Section 1.4 Graphs of Linear Inequalities A Linear Inequality and its Graph A linear inequality has the same form as a linear equation, except that the equal symbol is replaced with any one of,,

More information

Warm Up. Write an equation given the slope and y-intercept. Write an equation of the line shown.

Warm Up. Write an equation given the slope and y-intercept. Write an equation of the line shown. Warm Up Write an equation given the slope and y-intercept Write an equation of the line shown. EXAMPLE 1 Write an equation given the slope and y-intercept From the graph, you can see that the slope is

More information

Homework #1 Solutions

Homework #1 Solutions Homework #1 Solutions Problems Section 1.1: 8, 10, 12, 14, 16 Section 1.2: 2, 8, 10, 12, 16, 24, 26 Extra Problems #1 and #2 1.1.8. Find f (5) if f (x) = 10x x 2. Solution: Setting x = 5, f (5) = 10(5)

More information

Graphing Linear Equations in Two Variables

Graphing Linear Equations in Two Variables Math 123 Section 3.2 - Graphing Linear Equations Using Intercepts - Page 1 Graphing Linear Equations in Two Variables I. Graphing Lines A. The graph of a line is just the set of solution points of the

More information

Name: Date: Block: Midterm Exam Review Sheet 1

Name: Date: Block: Midterm Exam Review Sheet 1 Name: Date: Block: Midterm Exam Review Sheet 1 Chapter 1 1. Write a variable expression for 2. Simplify: 8 3 2 4 seven divided by the sum of x and five 3. Write an algebraic expression for 4. Write an

More information

Concept 7: Writing Linear Equations

Concept 7: Writing Linear Equations Concept 7: Writing Linear Equations Level 2 1. Watch the video (Writing Linear Equations: Level 2) 2. Complete the Notes & Basic Practice 3. Complete 2 of the following tasks IXL Practice Worksheets Creating

More information

Math Common Core Sampler Test

Math Common Core Sampler Test Math Common Core Sampler Test Our grade 8 sampler covers the twenty most common questions that we see targeted for this level in multiple choice format. For complete tests and break downs of each section,

More information

LINEAR EQUATIONS IN TWO VARIABLES

LINEAR EQUATIONS IN TWO VARIABLES 66 MATHEMATICS CHAPTER 4 LINEAR EQUATIONS IN TWO VARIABLES The principal use of the Analytic Art is to bring Mathematical Problems to Equations and to exhibit those Equations in the most simple terms that

More information

Key Terms: Quadratic function. Parabola. Vertex (of a parabola) Minimum value. Maximum value. Axis of symmetry. Vertex form (of a quadratic function)

Key Terms: Quadratic function. Parabola. Vertex (of a parabola) Minimum value. Maximum value. Axis of symmetry. Vertex form (of a quadratic function) Outcome R3 Quadratic Functions McGraw-Hill 3.1, 3.2 Key Terms: Quadratic function Parabola Vertex (of a parabola) Minimum value Maximum value Axis of symmetry Vertex form (of a quadratic function) Standard

More information

Practice Problems for Exam 1 Math 140A, Summer 2014, July 2

Practice Problems for Exam 1 Math 140A, Summer 2014, July 2 Practice Problems for Exam 1 Math 140A, Summer 2014, July 2 Name: INSTRUCTIONS: These problems are for PRACTICE. For the practice exam, you may use your book, consult your classmates, and use any other

More information

Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20 Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding

More information

Worksheet A5: Slope Intercept Form

Worksheet A5: Slope Intercept Form Name Date Worksheet A5: Slope Intercept Form Find the Slope of each line below 1 3 Y - - - - - - - - - - Graph the lines containing the point below, then find their slopes from counting on the graph!.

More information

Algebra 1 Topic 8: Solving linear equations and inequalities Student Activity Sheet 1; use with Overview

Algebra 1 Topic 8: Solving linear equations and inequalities Student Activity Sheet 1; use with Overview Algebra 1 Topic 8: Student Activity Sheet 1; use with Overview 1. A car rental company charges $29.95 plus 16 cents per mile for each mile driven. The cost in dollars of renting a car, r, is a function

More information

Educational Transfer Plan IISME Summer Fellowship Investigating Liner Equations Using Graphing Calculator

Educational Transfer Plan IISME Summer Fellowship Investigating Liner Equations Using Graphing Calculator Joumana Alsumidaie Fisher Middle School Algebra 1 Educational Transfer Plan IISME Summer Fellowship 2005 Investigating Liner Equations Using Graphing Calculator Overview: Investigating Linear Equations

More information

Algebra I: Strand 2. Linear Functions; Topic 2. Formalizing Slope and y-intercept; Task

Algebra I: Strand 2. Linear Functions; Topic 2. Formalizing Slope and y-intercept; Task 1 TASK : DESCRIBE STACKING CUPS Solutions Make a scatter plot of the data. Write a symbolic function rule and a verbal description of the situation. 1. 1 1 1 Number of Cups 0.5 1 6.0 2 8.5 11.0 2.5 2.5

More information

Course Title: Honors Algebra Course Level: Honors Textbook: Algebra 1 Publisher: McDougall Littell

Course Title: Honors Algebra Course Level: Honors Textbook: Algebra 1 Publisher: McDougall Littell Course Title: Honors Algebra Course Level: Honors Textbook: Algebra Publisher: McDougall Littell The following is a list of key topics studied in Honors Algebra. Identify and use the properties of operations

More information

High School Mathematics Algebra

High School Mathematics Algebra High School Mathematics Algebra This course is designed to give students the foundation of understanding algebra at a moderate pace. Essential material will be covered to prepare the students for Geometry.

More information

Revision Coordinate Geometry. Question 1: The gradient of the line joining the points V (k, 8) and W (2, k +1) is is.

Revision Coordinate Geometry. Question 1: The gradient of the line joining the points V (k, 8) and W (2, k +1) is is. Question 1: 2 The gradient of the line joining the points V (k, 8) and W (2, k +1) is is. 3 a) Find the value of k. b) Find the length of VW. Question 2: A straight line passes through A( 2, 3) and B(

More information

Tennessee Department of Education. Task: Sally s Car Loan

Tennessee Department of Education. Task: Sally s Car Loan Tennessee Department of Education Task: Sally s Car Loan Sally bought a new car. Her total cost including all fees and taxes was $15,. She made a down payment of $43. She financed the remaining amount

More information

2-4 Writing Linear Equations. Write an equation in slope-intercept form for the line described. 2. passes through ( 2, 3) and (0, 1) SOLUTION:

2-4 Writing Linear Equations. Write an equation in slope-intercept form for the line described. 2. passes through ( 2, 3) and (0, 1) SOLUTION: Write an equation in slope-intercept form for the line described 2 passes through ( 2, 3) and (0, 1) Substitute m = 1 and in the point slope form 4 passes through ( 8, 2); Substitute m = and (x, y) = (

More information

McMurry University Pre-test Practice Exam. 1. Simplify each expression, and eliminate any negative exponent(s).

McMurry University Pre-test Practice Exam. 1. Simplify each expression, and eliminate any negative exponent(s). 1. Simplify each expression, and eliminate any negative exponent(s). a. b. c. 2. Simplify the expression. Assume that a and b denote any real numbers. (Assume that a denotes a positive number.) 3. Find

More information

MATH 65 NOTEBOOK CERTIFICATIONS

MATH 65 NOTEBOOK CERTIFICATIONS MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1

More information

Systems of Linear Equations. Suggested Time: 11 Hours

Systems of Linear Equations. Suggested Time: 11 Hours Systems of Linear Equations Suggested Time: 11 Hours Unit Overview Focus and Context In this unit, students will model a situation with a linear system and use the equations to solve a related problem.

More information

c sigma & CEMTL

c sigma & CEMTL c sigma & CEMTL Foreword The Regional Centre for Excellence in Mathematics Teaching and Learning (CEMTL) is collaboration between the Shannon Consortium Partners: University of Limerick, Institute of Technology,

More information

Linear Approximations ACADEMIC RESOURCE CENTER

Linear Approximations ACADEMIC RESOURCE CENTER Linear Approximations ACADEMIC RESOURCE CENTER Table of Contents Linear Function Linear Function or Not Real World Uses for Linear Equations Why Do We Use Linear Equations? Estimation with Linear Approximations

More information

Part 1: Background - Graphing

Part 1: Background - Graphing Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software 1 1.1 Graphing Part 1: Background - Graphing In science it is very important to find and

More information

Topic 15 Solving System of Linear Equations

Topic 15 Solving System of Linear Equations Topic 15 Solving System of Linear Equations Introduction: A Linear Equation is an equation that contains two variables, typically x and y that when they are graphed on a cartesian grid make a straight

More information

CHAPTER 1 Linear Equations

CHAPTER 1 Linear Equations CHAPTER 1 Linear Equations 1.1. Lines The rectangular coordinate system is also called the Cartesian plane. It is formed by two real number lines, the horizontal axis or x-axis, and the vertical axis or

More information

Graphs of Proportional Relationships

Graphs of Proportional Relationships Graphs of Proportional Relationships Student Probe Susan runs three laps at the track in 12 minutes. A graph of this proportional relationship is shown below. Explain the meaning of points A (0,0), B (1,),

More information

CHAPTER 2: POLYNOMIAL AND RATIONAL FUNCTIONS

CHAPTER 2: POLYNOMIAL AND RATIONAL FUNCTIONS CHAPTER 2: POLYNOMIAL AND RATIONAL FUNCTIONS 2.01 SECTION 2.1: QUADRATIC FUNCTIONS (AND PARABOLAS) PART A: BASICS If a, b, and c are real numbers, then the graph of f x = ax2 + bx + c is a parabola, provided

More information

Quadratic Function Parabola Shape

Quadratic Function Parabola Shape Axis of Symmetry MA 158100 Lesson 8 Notes Summer 016 Definition: A quadratic function is of the form f(x) = y = ax + bx + c; where a, b, and c are real numbers and a 0. This form of the quadratic function

More information

PRESENTED BY THE NUMEROLOGIST Mathematics, Grade 9. Welcome to today s topic Parts of Listen & Learn. Presentation, questions, Q&A

PRESENTED BY THE NUMEROLOGIST Mathematics, Grade 9. Welcome to today s topic Parts of Listen & Learn. Presentation, questions, Q&A Number Sense and Numeration PRESENTED BY THE NUMEROLOGIST Mathematics, Grade 9 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping NOT the Chat Room Your questions

More information