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

Size: px
Start display at page:

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

Transcription

1 Math "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 graphing. * General form of the equation of a line. Preliminaries: Slope of a Line: The slope of a line passing through points (x 1, y 1 ) and (x 2, y 2 ) is m = rise run = y 2 y 1 x 2 x 1 (where x 1 x 2 ) Also, we will use two facts from section 2.3: - Different lines having the same slope are parallel m 1 = m 2. - If the slopes of two lines are negative reciprocals, the lines are perpendicular m 1 = 1 m 2 or m 1 m 2 = 1. Definition: Standard (General) Form of a Linear Equation A linear equation in two variables is an equation that can be written in the form where A, B, and C are real numbers and A and B are not both zero. Ax + By = C Use the Point-Slope Form to Write the Equation of a Line Point-Slope Form: The equation of the line passing through (x 1, y 1 ) and with slope m is Example 1: (Using the point-slope form) Find an equation of the line that has slope 5 and passes trough (2, 6). Write the equation in standard form. Example 2: (Using the point-slope form) Find an equation of the line passing through ( 2, 5) and (, 3). Page: 1

2 Page: 2 Use Slope-Intercept Form to Write the Equation of a Line Slope-Intercept Form The equation of the line with slope m and y intercept (0, b) is Example 3: (Using the slope-intercept form) Use the slope-intercept form to write an equation of the line with slope 5 ( and y intercept 0, 1 ). Write the answer in standard form. Example : (Using the slope-intercept form) Find the slope and y-intercept of the line graphed below. line. Write the answer in standard form. y 5 Then use the slope-intercept form to write the equation of the x Example 5: (Using the slope-intercept form) Use the slope-intercept form to write an equation of the line that has the given slope and passes through the given point. a) slope 3; and passes through ( 2, 5) b) slope 2; and passes through ( 2, 8)

3 Page: 3 Example 6: (Applications) After purchasing a new drill press, a machine shop owner had his accountant prepare a depreciation worksheet for tax purposes. Depreciation Worksheet Drill press... $1,970 (new) Salvage value... $270 (in 10 years) a) Assuming straight-line depreciation, write an equation that gives the value (v) of the drill press after x years of use. b) Find the value of the drill press after years of use. Use Slope as an Aid When Graphing If we know the slope and the y intercept of a line, we can graph the line without constructing a table of solutions. Example 7: (Use slope as an aid when graphing) Find the slope and y-intercept of the line with the equation 3x 2y = and graph the line. y x

4 Page: Recognize Parallel and Perpendicular Lines Example 8: (Using slopes to recognize parallel and perpendicular lines) Show that the lines represented by 2y = 3x + 12 and 6x + y = 7 are parallel. Example 9: (Using slopes to recognize parallel and perpendicular lines) Show that the lines represented by 3x + 2y = 6 and 2x 3y = 6 are perpendicular. Example 10: (Using slopes to find the equation of parallel and perpendicular lines) Find the equation of the line that passes through ( 6, 3) and is perpendicular to the line y + 3x = 12. Write the equation in slope-intercept form.

5 Page: 5 Example 11: (Using slopes to find the equation of parallel and perpendicular lines) Find the equation of the line that passes through ( 2, 5) and is parallel to the line y = 8x 3. Write the equation in slope-intercept form. When we are asked to write the equation of a line, we first must determine what we know about the graph of the line: its slope, its y-intercept, points it passes through, and so on. Then substitute the appropriate numbers into one of the following forms of a linear equation. Forms of a Linear Equation Standard Form A 0 and B 0 Slope-Intercept Form slope = m and y intercept is (0, b) Point-Slope Form slope = m and the line passes through (x 1, y 1 ) A Horizontal Line m = 0 and the y intercept is (0, b) A Vertical Line m = undefined and the x intercept is (a, 0)

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

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

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

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

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

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

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

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

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

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

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

Math 154 :: Elementary Algebra

Math 154 :: Elementary Algebra Math :: Elementary Algebra Section. Section. Section. Section. Section. Math :: Elementary Algebra Section. The Rectangular (Cartesian) Coordinate System. The variable x usually represents the independent

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

Outcome 9 Review Foundations and Pre-Calculus 10

Outcome 9 Review Foundations and Pre-Calculus 10 Outcome 9 Review Foundations and Pre-Calculus 10 Level 2 Example: Writing an equation in slope intercept form Slope-Intercept Form: y = mx + b m = slope b = y-intercept Ex : Write the equation of a line

More 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

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

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

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

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

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

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

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

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

(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

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

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

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

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

Graphing Lines with a Table

Graphing Lines with a Table Graphing Lines with a Table Select (or use pre-selected) values for x Substitute those x values in the equation and solve for y Graph the x and y values as ordered pairs Connect points with a line Graph

More 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

In this section, we find equations for straight lines lying in a coordinate plane.

In this section, we find equations for straight lines lying in a coordinate plane. 2.4 Lines Lines In this section, we find equations for straight lines lying in a coordinate plane. The equations will depend on how the line is inclined. So, we begin by discussing the concept of slope.

More information

Section 2.3 Task List

Section 2.3 Task List Summer 2017 Math 108 Section 2.3 67 Section 2.3 Task List Work through each of the following tasks, carefully filling in the following pages in your notebook. Section 2.3 Function Notation and Applications

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

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

Review for Mastery. Identifying Linear Functions

Review for Mastery. Identifying Linear Functions Identifying Linear Functions You can determine if a function is linear by its graph, ordered pairs, or equation. Identify whether the graph represents a linear function. Step 1: Determine whether the graph

More 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

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

Slopes of of Parallel and and Perpendicular Lines Lines Holt Algebra 1

Slopes of of Parallel and and Perpendicular Lines Lines Holt Algebra 1 5-8 Slopes of of Parallel and and Lines Warm Up Lesson Presentation Lesson Quiz Bell Quiz 5-8 Find the reciprocal. 1. 2 2. 1 pt 1 pt 1 pt 3. 2 pts 2 pts 2 pts Find the slope of the line that passes through

More 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

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

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

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

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 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

Aim #35.1: How do we graph using a table?

Aim #35.1: How do we graph using a table? A) Take out last night's homework Worksheet - Aim 34.2 B) Copy down tonight's homework Finish aim 35.1 Aim #35.1: How do we graph using a table? C) Plot the following points... a) (-3, 5) b) (4, -2) c)

More 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

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

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

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

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 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

Outcome 7 Review. *Recall that -1 (-5) means

Outcome 7 Review. *Recall that -1 (-5) means Outcome 7 Review Level 2 Determine the slope of a line that passes through A(3, -5) and B(-2, -1). Step 1: Remember that ordered pairs are in the form (x, y). Label the points so you can substitute into

More information

Linear Equations in Two Variables

Linear Equations in Two Variables Using Slope Linear Equations in Two Variables CHAT Pre-Calculus Section. The siplest atheatical odel for relating two variables is linear equation in two variables. It is called a linear equation because

More information

Equations of Lines and Linear Models

Equations of Lines and Linear Models 8. Equations of Lines and Linear Models Equations of Lines If the slope of a line and a particular point on the line are known, it is possible to find an equation of the line. Suppose that the slope of

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

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

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

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

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

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

Geometry Unit 3 Note Sheets Date Name of Lesson. Slopes of Lines. Partitioning a Segment. Equations of Lines. Quiz

Geometry Unit 3 Note Sheets Date Name of Lesson. Slopes of Lines. Partitioning a Segment. Equations of Lines. Quiz Date Name of Lesson Slopes of Lines Partitioning a Segment Equations of Lines Quiz Introduction to Parallel and Perpendicular Lines Slopes and Parallel Lines Slopes and Perpendicular Lines Perpendicular

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

You re the Teacher. Writing Equations with Specific Characteristics. Word Problem Worksheet

You re the Teacher. Writing Equations with Specific Characteristics. Word Problem Worksheet Name # Accelerated Algebra: Marking Period 2 Choice Board Per. 150 points Directions: Create a TIC-TAC-TOE (up and down, left and right, or diagonal) to complete THREE total tasks. Each task is worth 50

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

1. Graph y = 2x 3. SOLUTION: The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept.

1. Graph y = 2x 3. SOLUTION: The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. 1. Graph y = 2x 3. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. Plot the y-intercept (0, 3). The slope is. From (0, 3), move up 2 units and right 1

More information

PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to find key features. The table of values is shown below:

PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to find key features. The table of values is shown below: Math (L-3a) Learning Targets: I can find the vertex from intercept solutions calculated by quadratic formula. PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to

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

Slopes of Lines Notes What is slope?

Slopes of Lines Notes What is slope? Slopes of Lines Notes What is slope? Find the slope of each line. 1 Find the slope of each line. Find the slope of the line containing the given points. 6, 2!!"#! 3, 5 4, 2!!"#! 4, 3 Find the slope of

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

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

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

Study Guide: Slope and Linear Equations

Study Guide: Slope and Linear Equations Rates and Unit Rates A rate is a proportional relationship between two quantities. Unit rate is a rate where the second quantity is 1. Example: Pauline can mow 35 square feet of lawn is 2.5 minutes. (this

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

Section 1.3. Slope of a Line

Section 1.3. Slope of a Line Slope of a Line Introduction Comparing the Steepness of Two Objects Two ladders leaning against a building. Which is steeper? We compare the vertical distance from the base of the building to the ladder

More information

Student Exploration: Standard Form of a Line

Student Exploration: Standard Form of a Line Name: Date: Student Exploration: Standard Form of a Line Vocabulary: slope, slope-intercept form, standard form, x-intercept, y-intercept Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1.

More information

t s time we revisit our friend, the equation of a line: y = mx + b

t s time we revisit our friend, the equation of a line: y = mx + b CH PARALLEL AND PERPENDICULAR LINES INTRODUCTION I t s time we revisit our friend, the equation of a line: mx + b SLOPE -INTERCEPT To be precise, b is not the -intercept; b is the -coordinate of the -intercept.

More information

Then finding the slope, we can just use the same method that we have done the other ones we get the slope 4 1

Then finding the slope, we can just use the same method that we have done the other ones we get the slope 4 1 169 Graphing Equations with Slope Okay, now that you know how to graph a line by getting some points, and you know how to find the slope between two points, you should be able to find the slope of a line

More information

Study Guide: Slope and Linear Equations

Study Guide: Slope and Linear Equations Rates and Unit Rates A rate is a proportional relationship between two quantities. Unit rate is a rate where the second quantity is 1. Example: Pauline can mow 35 square feet of lawn is 2.5 minutes. (this

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

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

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

5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs

5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs Chapter 5: Trigonometric Functions and Graphs 1 Chapter 5 5.1 Graphing Sine and Cosine Functions Pages 222 237 Complete the following table using your calculator. Round answers to the nearest tenth. 2

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

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

Parallel Postulate. Perpendicular Postulate PARALLEL AND SKEW LINES WITH PARALLEL PLANES. Lines m and n are. Lines m and k are. Planes T and U are.

Parallel Postulate. Perpendicular Postulate PARALLEL AND SKEW LINES WITH PARALLEL PLANES. Lines m and n are. Lines m and k are. Planes T and U are. Unit 6: Parallel and Perpendicular Lines Lesson 6.1: Identify Pairs of Lines and Angles Lesson 3.1 from textbook Objectives Identify relationships between lines such as parallel and skew. Understand and

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

A A B B C C D D. NC Math 2: Transformations Investigation

A A B B C C D D. NC Math 2: Transformations Investigation NC Math 2: Transformations Investigation Name # For this investigation, you will work with a partner. You and your partner should take turns practicing the rotations with the stencil. You and your partner

More information

8.2 Slippery Slopes. A Solidify Understanding Task

8.2 Slippery Slopes. A Solidify Understanding Task 7 8.2 Slippery Slopes A Solidify Understanding Task CC BY https://flic.kr/p/kfus4x While working on Is It Right? in the previous module you looked at several examples that lead to the conclusion that the

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

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

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

Contents Systems of Linear Equations and Determinants

Contents Systems of Linear Equations and Determinants Contents 6. Systems of Linear Equations and Determinants 2 Example 6.9................................. 2 Example 6.10................................ 3 6.5 Determinants................................

More information

Chapter 2 Review WS Period: Date:

Chapter 2 Review WS Period: Date: Geometry Name: Chapter 2 Review WS Period: Date:. A transversal intersects two parallel lines. The measures of a pair of alternate interior angles are 5v and 2w. The measures of a pair of same-side exterior

More information

Algebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form.

Algebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form. T328 [OBJECTIVE] The student will graph lines described by equations in standard form. [MATERIALS] Student pages S125 S133 Transparencies T336, T338, T340, T342, T344 Wall-size four-quadrant grid [ESSENTIAL

More 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

Chapter 9. Conic Sections and Analytic Geometry. 9.1 The Ellipse. Copyright 2014, 2010, 2007 Pearson Education, Inc.

Chapter 9. Conic Sections and Analytic Geometry. 9.1 The Ellipse. Copyright 2014, 2010, 2007 Pearson Education, Inc. Chapter 9 Conic Sections and Analytic Geometry 9.1 The Ellipse Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Graph ellipses centered at the origin. Write equations of ellipses in standard

More information

Algebra I CC Exam Review #1 H o2m0b1l3v 7KRu9tmal NSIoffrtGwaafrKeB 5LZLhCe.h m na3ldll 3rPiagBhlt8sm 4rEe0sPevr3vKe6dR.S. y x y. ( k ) ( 10) ( ) ( )

Algebra I CC Exam Review #1 H o2m0b1l3v 7KRu9tmal NSIoffrtGwaafrKeB 5LZLhCe.h m na3ldll 3rPiagBhlt8sm 4rEe0sPevr3vKe6dR.S. y x y. ( k ) ( 10) ( ) ( ) -1-5 b2e0r143a qkxustsah YS3ogfrtFwiazr9e3 BLjLPCQ.W R paslllj LrkiTgphqtysN drzeosqegrqvcezdj.o I YMOaPdyev LwhiVtthR AINnXfriknHirtleD famlwgue4bsryas e2r.j Worksheet by Kuta Software LLC Algebra I CC

More information

Slope. Plug In. Finding the Slope of a Line. m 5 1_ 2. The y-intercept is where a line

Slope. Plug In. Finding the Slope of a Line. m 5 1_ 2. The y-intercept is where a line LESSON Slope Plug In Finding the Slope of a Line The slope of a line is the ratio of the change in the -values to the change in the corresponding -values. 0 7 8 change in -values Slope change in -values

More 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