Math 154 :: Elementary Algebra

Size: px
Start display at page:

Download "Math 154 :: Elementary Algebra"

Transcription

1 Math :: Elementary Algebra Section. Section. Section. Section. Section.

2 Math :: Elementary Algebra Section. The Rectangular (Cartesian) Coordinate System. The variable x usually represents the independent variable. The horizontal axis is used to represent the independent variable. The value of this variable represents a left/right movement.. The variable y usually represents the dependent variable. The vertical axis is used to represent the dependent variable. The value of this variable represents an up/down movement.. The points on a rectangular (Cartesian) coordinate system are called ordered pairs because they are always listed in order... A, 0 ; B, 6 ; C, ; D, ; E 0, 6. A 0, 0 ; B 0, 0 ; C 0, 0 ; D 70, 0 ; E 60, 0 7. Section. Answers

3 Math :: Elementary Algebra Section. Answers

4 Math :: Elementary Algebra Section. Graphing Linear Equations in Two-variables. This answer should be in your own words.. This answer should be in your own words.. This answer should be in your own words.. This answer should be in your own words.. xy 0 a), 0 is a solution. b), is a solution. c) 0, is not a solution. d), is a solution. e), is not a solution. 6. y x, is not a solution. a) b), 0 is a solution. c) 0, is a solution. d), is not a solution. e), is a solution. 7. y a), 0 is not a solution. b) 0, is a solution. c), is not a solution. d), is a solution. e), is a solution. Section. Answers

5 Math :: Elementary Algebra 8. xy 9. yx 6 0. y. y x Section. Answers

6 Math :: Elementary Algebra. xy. x y. y x. x y Section. Answers

7 Math :: Elementary Algebra 6. x 7. y x 8. x y 9. y x Section. Answers 6

8 Math :: Elementary Algebra 0. xy 0. y 6. x. xy 6 Section. Answers 7

9 Math :: Elementary Algebra. x y 0. xy 6. yx 8 7. x y Section. Answers 8

10 Math :: Elementary Algebra 8. x y 9. x y 0. x y Section. Answers 9

11 Math :: Elementary Algebra Section. Intercepts and Slope. This answer should be in your own words.. This answer should be in your own words.. This answer should be in your own words.. The slope of any horizontal line is 0.. The slope of any vertical line is undefined. 6. This answer should be in your own words. 7. This answer should be in your own words. 0, ; slope: 8. x-intercept:,0 ; y-intercept: 9. x-intercept: none ; y-intercept: 0, ; slope: 0 0. x-intercept: 6,0 ; y-intercept: 0, ; slope:. x-intercept:,0 ; y-intercept: none ; slope: undefined. x-intercept: 60,0 ; y-intercept: 0, 0 ; slope:. x-intercept: 6,0 ; y-intercept: 0,. x-intercept:,0 ; y-intercept: 0, 0. x-intercept:,0 ; y-intercept: 0, 6. x-intercept: 8,0 ; y-intercept: 0, 7. x-intercept: none; y-intercept: 0,0 8. x-intercept: 9 9. x-intercept:,0 ; y-intercept: none 0. x-intercept:,0 ; y-intercept: 0, ; slope: ; slope: 0. x-intercept: 0,0 ; y-intercept: 0, Section. Answers 0

12 Math :: Elementary Algebra. x-intercept:,0 ; y-intercept: 0,. x-intercept:,0 ; y-intercept: none. x-intercept: 0,0 ; y-intercept: 0,0. x-intercept: none; y-intercept: 0,0 Section. Answers

13 Math :: Elementary Algebra 6. x-intercept:,0 ; y-intercept: 0, 7. m 8. m 9. m 0 0. m. m 6. m 6. undefined. m. m 0 6. m 7. m 8. undefined 9. m 0. m. m 0. m 8. neither parallel nor perpendicular. perpendicular. neither parallel nor perpendicular 6. parallel 7. neither parallel nor perpendicular 8. Line : m ; Line : m 8 8 ; perpendicular 9. Line : m ; Line : m ; parallel 0. Line : m ; Line : m ; neither parallel nor perpendicular. Line : m 0 ; Line : m undefined; perpendicular Section. Answers

14 Math :: Elementary Algebra Section. Equations of Lines. The slope-intercept form of a linear equation is y mx b.. The point-slope form of a linear equation is y y mx x.. This answer should be in your own words.. This answer should be in your own words.. The slope of a horizontal line is 0. The general form of the equation of a horizontal line is y = a constant. 6. The slope of a vertical line is undefined. The general form of the equation of a vertical line is x = a constant. 7. If you plan to use slope-intercept form of a linear equation to write the equation of a line, you must find the slope and the y- intercept of that line before you write the equation. 8. If you plan to use point-slope form of a linear equation to write the equation of a line, you must find the slope and a point on that line before you write the equation. 9. slope: ; y-intercept: 0, 7 0. slope: ; y-intercept: 0,. slope: ; y-intercept: 0,. slope: ; y-intercept: 0,. slope: ; y-intercept: 0,. slope: ; y-intercept: 0,. slope: 0 ; y-intercept: 0, 6. slope: 7 ; y-intercept: 0,6 7. slope: ; y-intercept: 0, 8. x-intercept: 6,0 ; y-intercept: 9. x-intercept:,0 ; y-intercept: 0, 0, ; slope: ; equation: y x ; slope: ; equation: y x 0. x-intercept: none ; y-intercept: 0, ; slope: 0 ; equation: y ; y-intercept: 0, ; slope: y. x-intercept:,0. 9 x-intercept: ; equation: x,0 ; y-intercept: none ; slope: undefined ; equation: 9 x. x-intercept: 60,0 ; y-intercept:. yx 0, 0 ; slope: ; equation: y x 0 Section. Answers

15 Math :: Elementary Algebra. y x 6. y x 7. y x 8. y Section. Answers

16 Math :: Elementary Algebra 9. 8 x 0. xy. y x. xy Section. Answers

17 Math :: Elementary Algebra. y. 0x0 y 0. xy 6. x y Section. Answers 6

18 Math :: Elementary Algebra 7. x y 8. 8x y 9. 9 y x 0. xy Section. Answers 7

19 Math :: Elementary Algebra. 6 y x. y x 7 6. y x. y x. y 6. x 7. yx 9 8. y x 9. y x 9 0. yx. y x. y x. y. y x. yx 6. x 7. yx 8. y x 9. yx 60. y x 9 6. y x 0 6. yx 7 6. y x 7 6. y x 6. y x 66. y x 67. y x 68. y x Section. Answers 8

20 Math :: Elementary Algebra Section. Application Problems of Linear Equations in Two-Variables. feet per second. dollar per tickets. decreasing miles per hours, or 0.8 mile per hour. adults per children. a) y 0.x ; b) 90 tickets 6. a) C m 0 ; b) $7 ; c) 6 miles 7. a) CT 60 ; b) $80 chirps per minute ; c) 60 F 8. a) N p 7 ; b) 00 necklaces ; c) $900 ; d) $6 each ; e) $70 ; f) 7 necklaces for $ eac 9. a) T a ; b) 7 F ; c),000 feet 00 9 Section. Answers 9

Math 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 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 information

Chapter 2: Functions and Graphs Lesson Index & Summary

Chapter 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 information

Plotting 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 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 information

LINEAR EQUATIONS IN TWO VARIABLES

LINEAR 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 information

Section 3.5. Equations of Lines

Section 3.5. Equations of Lines Section 3.5 Equations of Lines Learning objectives Use slope-intercept form to write an equation of a line Use slope-intercept form to graph a linear equation Use the point-slope form to find an equation

More information

Chapter 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 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 information

Section 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.

Section 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 information

Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011.

Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. Warm-Up Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. You have 20 minutes at the beginning of class to work on these three tasks.

More information

2. To receive credit on any problem, you must show work that explains how you obtained your answer or you must explain how you obtained your answer.

2. To receive credit on any problem, you must show work that explains how you obtained your answer or you must explain how you obtained your answer. Math 50, Spring 2006 Test 2 PRINT your name on the back of the test. Circle your class: MW @ 11 TTh @ 2:30 Directions 1. Time limit: 50 minutes. 2. To receive credit on any problem, you must show work

More information

MATH 150 Pre-Calculus

MATH 150 Pre-Calculus MATH 150 Pre-Calculus Fall, 2014, WEEK 5 JoungDong Kim Week 5: 3B, 3C Chapter 3B. Graphs of Equations Draw the graph x+y = 6. Then every point on the graph satisfies the equation x+y = 6. Note. The graph

More information

Chapter 3 Linear Equations in Two Variables

Chapter 3 Linear Equations in Two Variables Chapter Linear Equations in Two Variables. Check Points. 6. x y x ( x, y) y ( ) 6, 6 y ( ), 0 y (0) 0, y () 0,0 y (),. E(, ) F(,0) G (6,0). a. xy 9 ( ) 9 69 9 9, true (, ) is a solution. b. xy 9 () 9 99

More information

Use the Point-Slope Form to Write the Equation of a Line

Use the Point-Slope Form to Write the Equation of a Line Math 90 8.3 "Writing Equations of Lines" Objectives: * Use the point-slope form to write the equation of a line. * Use the slope-intercept form to write the equation of a line. * Use slope as an aid when

More information

4.4 Equations of Parallel and Perpendicular

4.4 Equations of Parallel and Perpendicular www.ck12.org Chapter 4. Determining Linear Equations 4.4 Equations of Parallel and Perpendicular Lines Learning Objectives Determine whether lines are parallel or perpendicular. Write equations of perpendicular

More information

Algebra & Trig. 1. , then the slope of the line is given by

Algebra & 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 information

2.3 Quick Graphs of Linear Equations

2.3 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 information

Determine the intercepts of the line and ellipse below: Definition: An intercept is a point of a graph on an axis. Line: x intercept(s)

Determine 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 information

E. Slope-Intercept Form and Direct Variation (pp )

E. 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 information

PROPORTIONAL VERSUS NONPROPORTIONAL RELATIONSHIPS NOTES

PROPORTIONAL VERSUS NONPROPORTIONAL RELATIONSHIPS NOTES PROPORTIONAL VERSUS NONPROPORTIONAL RELATIONSHIPS NOTES Proportional means that if x is changed, then y is changed in the same proportion. This relationship can be expressed by a proportional/linear function

More information

The Picture Tells the Linear Story

The 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 information

Section 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 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 information

Lesson 11: Linear Functions, Part 2

Lesson 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 information

Use Slope-Intercept Form to Write the Equation of a Line

Use Slope-Intercept Form to Write the Equation of a Line Math 35 2. "Writing Equations of Lines" Objectives: * Use the slope-intercept form to write the equation of a line. * Use the point-slope form to write the equation of a line. * Use slope as an aid when

More information

Chapter 3 Graphing Linear Equations

Chapter 3 Graphing Linear Equations Chapter 3 Graphing Linear Equations Rectangular Coordinate System Cartesian Coordinate System Origin Quadrants y-axis x-axis Scale Coordinates Ex: Plot each point: (0,0), (-1, 3), (1, 3), (1, -3), (-1,

More information

Chapter 7, Part 1B Equations & Functions

Chapter 7, Part 1B Equations & Functions Chapter 7, Part 1B Equations & Functions Fingerstache Fingerstaches cost $7 per box. Copy and complete the table to find the cost of 2, 3, and 4 boxes. Number of Boxes Multiply by 7 Cost 1 1 x 7 $7 2 3

More information

Lesson 6.1 Linear Equation Review

Lesson 6.1 Linear Equation Review Name: Lesson 6.1 Linear Equation Review Vocabulary Equation: a math sentence that contains Linear: makes a straight line (no Variables: quantities represented by (often x and y) Function: equations can

More information

4 The Cartesian Coordinate System- Pictures of Equations

4 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 information

10 GRAPHING LINEAR EQUATIONS

10 GRAPHING LINEAR EQUATIONS 0 GRAPHING LINEAR EQUATIONS We now expand our discussion of the single-variable equation to the linear equation in two variables, x and y. Some examples of linear equations are x+ y = 0, y = 3 x, x= 4,

More information

Homework 5 - Section 3.3 #5

Homework 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 information

Actual testimonials from people that have used the survival guide:

Actual testimonials from people that have used the survival guide: Algebra 1A Unit: Coordinate Plane Assignment Sheet Name: Period: # 1.) Page 206 #1 6 2.) Page 206 #10 26 all 3.) Worksheet (SIF/Standard) 4.) Worksheet (SIF/Standard) 5.) Worksheet (SIF/Standard) 6.) Worksheet

More information

Math 152 Rodriguez Blitzer 2.5 The Point-Slope Form of the Equation of a Line

Math 152 Rodriguez Blitzer 2.5 The Point-Slope Form of the Equation of a Line Math 152 Rodriguez Blitzer 2.5 The Point-Slope Form of the Equation of a Line I. Point-Slope Form A. Linear equations we have seen so far: 1. standard form: Ax +By=C A, B, and C real numbers 2. slope-intercept

More information

MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points. Mr. Deyo Find Slope and Rate of Change

MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points. Mr. Deyo Find Slope and Rate of Change MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points Mr. Deyo Find Slope and Rate of Change Title: 5.5a Find Slope Given Two Points Date: Learning Target By the end of the period, I will find the slope

More information

6.1 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. 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 information

Lesson 1b Linear Equations

Lesson 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 information

Graphs, Linear Equations and Functions

Graphs, 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 information

A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal

A 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 information

Block: 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?

Block: 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 information

constant EXAMPLE #4:

constant EXAMPLE #4: Linear Equations in One Variable (1.1) Adding in an equation (Objective #1) An equation is a statement involving an equal sign or an expression that is equal to another expression. Add a constant value

More information

ACT Coordinate Geometry Review

ACT 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 information

y-intercept remains constant?

y-intercept remains constant? 1. The graph of a line that contains the points ( 1, 5) and (4, 5) is shown below. Which best represents this line if the slope is doubled and the y-intercept remains constant? F) G) H) J) 2. The graph

More information

Lesson 10 Practice Problems

Lesson 10 Practice Problems Name: Date: Lesson 10 Skills Practice 1. Determine the slope of the line between each of the following pairs of points. Show all steps, and reduce your answer to lowest terms. a. (4, 5) and ( 2, 3) b.

More information

CH 54 SPECIAL LINES. Ch 54 Special Lines. Introduction

CH 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 information

4.4 Slope and Graphs of Linear Equations. Copyright Cengage Learning. All rights reserved.

4.4 Slope and Graphs of Linear Equations. Copyright Cengage Learning. All rights reserved. 4.4 Slope and Graphs of Linear Equations Copyright Cengage Learning. All rights reserved. 1 What You Will Learn Determine the slope of a line through two points Write linear equations in slope-intercept

More information

MATH 021 TEST 2 REVIEW SHEET

MATH 021 TEST 2 REVIEW SHEET TO THE STUDENT: MATH 021 TEST 2 REVIEW SHEET This Review Sheet gives an outline of the topics covered on Test 2 as well as practice problems. Answers for all problems begin on page 8. In several instances,

More information

Welcome to Math! Put last night s homework on your desk and begin your warm-up (the other worksheet that you chose to save for today)

Welcome to Math! Put last night s homework on your desk and begin your warm-up (the other worksheet that you chose to save for today) Welcome to Math! Put last night s homework on your desk and begin your warm-up (the other worksheet that you chose to save for today) Unit Map - Geometry Thursday - Parallel Lines Cut by a Transversal

More information

4-7 Point-Slope Form. Warm Up Lesson Presentation Lesson Quiz

4-7 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 information

Creating a foldable for Equations of Lines

Creating a foldable for Equations of Lines Creating a foldable for Equations of Lines Equations of Lines Slope Direct Variation Slope-Intercept Form Standard Form Point-Slope Form Equation w/ slope & 1 point Equation w/ 2 points Horizontal & Vertical

More information

RECTANGULAR COORDINATE SYSTEM

RECTANGULAR COORDINATE SYSTEM RECTANGULAR COORDINATE SYSTEM Quadrant II (x0) 5 4 Quadrant I (x > 0, y>0) ORDERED PAIR: The first number in the ordered pair is the x- coordinate (aka abscissa) and the second number in the ordered

More information

1 Write a Function in

1 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 information

Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines

Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Two lines are if they are coplanar and do not intersect. Skew lines. Two

More information

Page 1 of 17 Name: Which graph does not represent a function of x? What is the slope of the graph of the equation y = 2x -? 2 2x If the point ( 4, k) is on the graph of the equation 3x + y = 8, find the

More information

REVIEW UNIT 4 TEST LINEAR FUNCTIONS

REVIEW UNIT 4 TEST LINEAR FUNCTIONS Name: Date: Page 1 of REVIEW UNIT 4 TEST LINEAR FUNCTIONS 1. Use the graph below to answer the following questions. a. Match each equation with line A, B, or C from the graph: A!!! =!! 1 B!! = 2! 2 = 3(!

More information

Ch. 6 Linear Functions Notes

Ch. 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 information

Graphs of linear equations will be perfectly straight lines. Why would we say that A and B are not both zero?

Graphs 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 information

Unit 10: The Equation of a Linear Function

Unit 10: The Equation of a Linear Function Section 10.1: The Equation of a Linear Function Section 10.2: Writing Linear Equations in Slope-Intercept Form Section 10.3: Parallel and Perpendicular Lines Section 10.4: Applications Slope-Intercept

More information

Name: Date: Block: Mid-Unit 4 Test Review All work must be shown for full credit.

Name: Date: Block: Mid-Unit 4 Test Review All work must be shown for full credit. Name: Date: Block: Mid-Unit 4 Test Review All work must be shown for full credit. 1) How do you have to walk so the motion detector graphs a straight line? Explain as clearly as you can. 2) What determines

More information

Graphing - Slope-Intercept Form

Graphing - Slope-Intercept Form 2.3 Graphing - Slope-Intercept Form Objective: Give the equation of a line with a known slope and y-intercept. When graphing a line we found one method we could use is to make a table of values. However,

More information

Unit 3 Algebra What is the y-intercept for the graph of the equation 3x 5y = 15?

Unit 3 Algebra What is the y-intercept for the graph of the equation 3x 5y = 15? Unit 3 lgebra 1 Name: ate: 1. The equation below is used to find (x, y) coordinates. y = 3x + 2 3. ennie is using this pattern to make stars for an laska state flag. Which coordinates could be found using

More information

Lesson 7 Slope-Intercept Formula

Lesson 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 information

Angles formed by Transversals

Angles formed by Transversals Section 3-1: Parallel Lines and Transversals SOL: None Objectives: Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal Vocabulary: Parallel

More information

Solving Equations and Graphing

Solving 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 information

Lesson 11 Practice Problems

Lesson 11 Practice Problems Lesson 11 Skills Practice 1. Determine the equation of the line between each of the following pairs of points. a. (4, 5) and (2, 3) b. ( 3, 2) and (1, 8) c. (5, 9) and (5, 2) d. (2, 1) and ( 2, 3) e. (4,

More information

(a) Find the equation of the line that is parallel to this line and passes through the point.

(a) Find the equation of the line that is parallel to this line and passes through the point. 1. Consider the line. (a) Find the equation of the line that is parallel to this line and passes through the point. (b) Find the equation of the line that is perpendicular to this line and passes through

More information

Study Guide and Review - Chapter 3. Find the x-intercept and y-intercept of the graph of each linear function.

Study 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 information

Since each element is paired with unique element in the range, it is a function.

Since each element is paired with unique element in the range, it is a function. 1. State the domain and range of the relation {( 3, 2), (4, 1), (0, 3), (5, 2), (2, 7)}. Then determine whether the relation is a function. The domain is the set of x-coordinates. The range is the set

More information

1.7 Parallel and Perpendicular Lines

1.7 Parallel and Perpendicular Lines Section 1.7 Parallel and Perpendicular Lines 11 Eplaining the Concepts 17. Name the five forms of equations of lines given in this section. 18. What tpe of line has one -intercept, but no -intercept? 19.

More information

ALGEBRA 1: CHAPTER 3 TEST

ALGEBRA 1: CHAPTER 3 TEST ALGEBRA 1: CHAPTER 3 TEST ANSWER SHEET Student Date. Period Your answers to Part I should be recorded on this answer sheet. Part I Answer all questions in this part. 1 6 2 7 3 4 5 8 9 10... Your answers

More information

MTH 103 Group Activity Problems (W2B) Name: Equations of Lines Section 2.1 part 1 (Due April 13) platform. height 5 ft

MTH 103 Group Activity Problems (W2B) Name: Equations of Lines Section 2.1 part 1 (Due April 13) platform. height 5 ft MTH 103 Group Activity Problems (W2B) Name: Equations of Lines Section 2.1 part 1 (Due April 13) Learning Objectives Write the point-slope and slope-intercept forms of linear equations Write equations

More information

MA Lesson 16 Sections 2.3 and 2.4

MA 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 information

3-5 Slopes of Lines. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry

3-5 Slopes of Lines. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry 3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the value of m. 1. 2. 3. 4. undefined 0 Objectives Find the slope of a line. Use slopes to identify parallel and perpendicular

More information

CHAPTER 3. Parallel & Perpendicular lines

CHAPTER 3. Parallel & Perpendicular lines CHAPTER 3 Parallel & Perpendicular lines 3.1- Identify Pairs of Lines and Angles Parallel Lines: two lines are parallel if they do not intersect and are coplaner Skew lines: Two lines are skew if they

More information

Practice A. Summer Income Use the following information. Decide which of the,two points 'lies on the graph of the line.

Practice A. Summer Income Use the following information. Decide which of the,two points 'lies on the graph of the line. NAME ~ ~ _ DATE Practice A For use withpages 216-217 Decide which of the,two points 'lies on the graph of the line. 1. x + Y = 8 2. 2x + Y = 8 3. Y - x = 2 a. (2,4) b. (2,6) a. (2,2) b. (3,2) a. (5, 3)

More information

Unit 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) 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 information

Review Journal 6 Assigned Work: Page 146, All questions

Review Journal 6 Assigned Work: Page 146, All questions MFM2P Linear Relations Checklist 1 Goals for this unit: I can explain the properties of slope and calculate its value as a rate of change. I can determine y-intercepts and slopes of given relations. I

More information

Lesson 15: The Slope of a Non Vertical Line

Lesson 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 information

Section 7B Slope of a Line and Average Rates of Change

Section 7B Slope of a Line and Average Rates of Change Section 7B Slope of a Line and Average Rates of Change IBM stock had a price of $186.91 at the end of September 2014. Over the next three months the stock price rose and fell and by the end of December

More information

3.1 parallel lines and transversals

3.1 parallel lines and transversals VOCAB Parallel lines- 3.1 parallel lines and transversals Skew lines- Parallel planes- Transversal- Interior < s Transversal Angle Pair Relationships Exterior < s Same side Interior < s (consecutive interiors

More information

Today We will: Create linear equations from a context and model with tables and graphs.

Today We will: Create linear equations from a context and model with tables and graphs. U2D11 Math 8C U2D11 Today We will: Create linear equations from a context and model with tables and graphs. U2D11 A quick review: Plotting Points Plot the points A(2, 3) B(-1, -4) C(-3, 3) C A D(4, -2)

More information

5. Determine the slope of a line that is perpendicular to the line through W( 9, 7) and X(6, 10). a. c. 15

5. Determine the slope of a line that is perpendicular to the line through W( 9, 7) and X(6, 10). a. c. 15 Math 101 Chapter 6 Review Multiple Choice Identif the choice that best completes the statement or answers the question. 1. Determine the slope of this line segment. A x 0 B. Determine the slope of the

More information

Lesson 11 Practice Problems

Lesson 11 Practice Problems Name: Date: Lesson 11 Skills Practice 1. Determine the equation of the line between each of the following pairs of points. a. (4, 5) and (2, 3) b. ( 3, 2) and (1, 8) c. (5, 9) and (5, 2) d. (2, 1) and

More information

Page 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 information

Chapter 7 Graphing Equations of Lines and Linear Models; Rates of Change Section 3 Using Slope to Graph Equations of Lines and Linear Models

Chapter 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 information

Use smooth curves to complete the graph between and beyond the vertical asymptotes.

Use smooth curves to complete the graph between and beyond the vertical asymptotes. 5.3 Graphs of Rational Functions Guidelines for Graphing Rational Functions 1. Find and plot the x-intercepts. (Set numerator = 0 and solve for x) 2. Find and plot the y-intercepts. (Let x = 0 and solve

More information

Algebra 1 Online:

Algebra 1 Online: Dear Algebra 2 Students, Within this packet you will find mathematical concepts and skills learned in Algebra 1 that are the foundation from which Algebra 2 is built. These concepts need to be reviewed

More information

Sect Linear Equations in Two Variables

Sect Linear Equations in Two Variables 99 Concept # Sect. - Linear Equations in Two Variables Solutions to Linear Equations in Two Variables In this chapter, we will examine linear equations involving two variables. Such equations have an infinite

More information

Using Slopes and Intercepts

Using 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 information

Chapter 3 Parallel and Perpendicular Lines Geometry. 4. For, how many perpendicular lines pass through point V? What line is this?

Chapter 3 Parallel and Perpendicular Lines Geometry. 4. For, how many perpendicular lines pass through point V? What line is this? Chapter 3 Parallel and Perpendicular Lines Geometry Name For 1-5, use the figure below. The two pentagons are parallel and all of the rectangular sides are perpendicular to both of them. 1. Find two pairs

More information

Chapter 3 Parallel and Perpendicular Lines

Chapter 3 Parallel and Perpendicular Lines Chapter 3 Parallel and Perpendicular Lines Parallel Lines Lines Parallel Symbol: Perpendicular Lines Lines that Perpendicular Symbol: Postulate 13: Parallel Postulate For any and a not on the line, there

More information

Name: 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 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 information

Unit 11: Linear Equations and Inequalities

Unit 11: Linear Equations and Inequalities Section 11.1: General Form ax + by = c Section 11.2: Applications General Form Section 11.3: Linear Inequalities in Two Variables Section 11.4: Graphing Linear Inequalities in Two Variables KEY TERMS AND

More information

SM3 Lesson 2-3 (Intercept Form Quadratic Equation)

SM3 Lesson 2-3 (Intercept Form Quadratic Equation) SM3 Lesson 2-3 (Intercept Form Quadratic Equation) Factor the following quadratic expressions: x 2 + 11x + 30 x 2 10x 24 x 2 8x + 15 Standard Form Quadratic Equation (x + 5)(x + 6) (x 12)(x + 2) (x 5)(x

More information

Tasks for this target will ask students to graph one or more proportional relationships and connect the unit rate(s) to the context of the problem.

Tasks for this target will ask students to graph one or more proportional relationships and connect the unit rate(s) to the context of the problem. Grade 8 Math C1 TC Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Expressions and

More information

Cumulative Review : MAT-032 (Algebra B) 2013

Cumulative Review : MAT-032 (Algebra B) 2013 Perform the indicated operations and simplify: ( 7. 8. 9. Add 10. Subtract from 1 Subtract from the sum of and 1 Subtract the sum of and from 7. 8. 9. 10. 1 1 Factor completely: 7. 8. 7. 8. Factor completely:

More information

Appendix M TERMINOLOGY. Slope of a Line. Slope. Undefined Slope. Slope-Intercept Form

Appendix 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 information

2.3 BUILDING THE PERFECT SQUARE

2.3 BUILDING THE PERFECT SQUARE 16 2.3 BUILDING THE PERFECT SQUARE A Develop Understanding Task Quadratic)Quilts Optimahasaquiltshopwhereshesellsmanycolorfulquiltblocksforpeoplewhowant tomaketheirownquilts.shehasquiltdesignsthataremadesothattheycanbesized

More information

Analytic Geometry ةيليلحتلا ةسدنھلا

Analytic Geometry ةيليلحتلا ةسدنھلا Analytic Geometry الھندسة التحليلية نظام اإلحداثيات الديكارتي 1-1 Cartesian Coordinate System The Cartesian coordinate system, or the rectangular coordinate system, is a geometrical system that is used

More information

Lesson 7A Slope-Intercept Formula

Lesson 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 information

Math Labs. Activity 1: Rectangles and Rectangular Prisms Using Coordinates. Procedure

Math Labs. Activity 1: Rectangles and Rectangular Prisms Using Coordinates. Procedure Math Labs Activity 1: Rectangles and Rectangular Prisms Using Coordinates Problem Statement Use the Cartesian coordinate system to draw rectangle ABCD. Use an x-y-z coordinate system to draw a rectangular

More information

Analytic Geometry. The x and y axes divide the Cartesian plane into four regions called quadrants.

Analytic Geometry. The x and y axes divide the Cartesian plane into four regions called quadrants. Analytic Geometry الھندسة التحليلية نظام اإلحداثيات الديكارتي 1-1 Cartesian Coordinate System The Cartesian coordinate system, or the rectangular coordinate system, is a geometrical system that is used

More information

Find the equation of a line given its slope and y-intercept. (Problem Set exercises 1 6 are similar.)

Find 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 information

Mathematics Success Grade 8

Mathematics 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 information