Equations of Lines - 3.4
|
|
|
- Dorthy Barker
- 5 years ago
- Views:
Transcription
1 Equations of Lines Fall Math 1010 y = mx + b (y y 1 ) = m(x x 1 ) Ax + By = C (Math 1010) M / 11
2 Roadmap Discussion/Activity: Graphs and linear equations. Form: The Point-Slope Equation Form: Vertical, Horizontal, Parallel, and Perpendicular Lines Applications Discussion on homework, quizzes, and exams. (Math 1010) M / 11
3 Point-Slope Recall the slope formula re-imagined without fractions. Slope: (y 2 y 1 ) = m(x 2 x 1 ) This formula becomes the point-slope equation of a line when a slope, m, is known along with only one point, (x 1, y 1 ). Point-slope form: (y y 1 ) = m(x x 1 ) (Math 1010) M / 11
4 Example - Point-Slope Write an equation of the line passing through the point (2, 7) with a slope of m = 4. (Math 1010) M / 11
5 Example - Point-Slope Write an equation of the line passing through the point (2, 7) with a slope of m = 4. y ( 7) = 4(x 2) (Math 1010) M / 11
6 Example - Point-Slope Write an equation of the line passing through the point (2, 7) with a slope of m = 4. y ( 7) = 4(x 2) y + 7 = 4(x 2) (Math 1010) M / 11
7 Example - Point-Slope Slope-intercept forms y = mx + b pass through the point (0, b). Then the point-slope form looks like:. y b = m(x 0) (Math 1010) M / 11
8 Example - Point-Slope Slope-intercept forms y = mx + b pass through the point (0, b). Then the point-slope form looks like:. y b = m(x 0) Write the point-slope form of the line through ( 2, 1) and (4, 2), then write its slope-intercept form. (Math 1010) M / 11
9 Example - Point-Slope Slope-intercept forms y = mx + b pass through the point (0, b). Then the point-slope form looks like:. y b = m(x 0) Write the point-slope form of the line through ( 2, 1) and (4, 2), then write its slope-intercept form. m = ( 2) = 1 6 y 1 = 1 (x + 2) 6 y = 1 6 x (Math 1010) M / 11
10 Special Forms Horizontal lines have a slope of y-coordinate b, from its Vertical lines have an a, from its (a, 0).. Each point has (0, b). slope. Each point has x-coordinate Euclid formulated geometric axioms, one of which is that there is only one line through a given point that is parallel to another line. Recall that parallel lines have equal slopes. Perpendicular lines have opposite-and-reciprocal slopes. (Math 1010) M / 11
11 Special Forms Horizontal lines have a slope of y-coordinate b, from its Vertical lines have an a, from its (a, 0).. Each point has (0, b). slope. Each point has x-coordinate Euclid formulated geometric axioms, one of which is that there is only one line through a given point that is parallel to another line. Recall that parallel lines have equal slopes. Perpendicular lines have opposite-and-reciprocal slopes. Blanks: zero, y-intercept, undefined, x-intercept (Math 1010) M / 11
12 Summary of Forms of Equations of Lines Algebraic Form y = mx + b Name of the Form Slope-Intercept (y y 1 ) = m(x x 1 ) Point-Slope Ax + By = C x = a y = b m 1 = m 2 m 1 = 1 m 2 Standard Form Vertical line Horizontal line Parallel lines Perpendicular lines (Math 1010) M / 11
13 Application - Depreciation The value of a car decreases in terms of time t. Let s assume this to be linear depeciation. Set-up: The car s initial value is $38,000. After 7 years it will be valued at $7,000. Write an equation for the straight-line depreciation of the value of the car. (Math 1010) M / 11
14 Application - Depreciation The value of a car decreases in terms of time t. Let s assume this to be linear depeciation. Set-up: The car s initial value is $38,000. After 7 years it will be valued at $7,000. Write an equation for the straight-line depreciation of the value of the car. Use the equation to find the value of the car 2 years from its initial value. (Math 1010) M / 11
15 Application - Depreciation The value of a car decreases in terms of time t. Let s assume this to be linear depeciation. Set-up: The car s initial value is $38,000. After 7 years it will be valued at $7,000. Write an equation for the straight-line depreciation of the value of the car. Use the equation to find the value of the car 2 years from its initial value. Graph the equation. When does the value of the car become $0? (Math 1010) M / 11
16 Application - Cost The total cost to produce x items combines the overhead cost and cost to produce one unit. Set-up: To make hats, the total cost is the sum of the overhead of $20 and unit cost of $6 per item. Write an equation for the total cost of producing x hats. (Math 1010) M / 11
17 Application - Cost The total cost to produce x items combines the overhead cost and cost to produce one unit. Set-up: To make hats, the total cost is the sum of the overhead of $20 and unit cost of $6 per item. Write an equation for the total cost of producing x hats. Use the equation to find the cost of make 40 products. (Math 1010) M / 11
18 Application - Cost The total cost to produce x items combines the overhead cost and cost to produce one unit. Set-up: To make hats, the total cost is the sum of the overhead of $20 and unit cost of $6 per item. Write an equation for the total cost of producing x hats. Use the equation to find the cost of make 40 products. A budget constraint of $300 is introduced. Use either the equation or its graph to estimate how many hats can be produced under this constraint. (Math 1010) M / 11
19 Application - Demand Demand relates the price p of a service and the demand d at that price. This relationship may be linear. Set-up: From 2010, raffle tickets priced at $4 sold 2000 tickets. From 2011, raffle tickets priced at $5 sold 1800 tickets. Write a linear equation for the demand of tickets sold priced at p dollars. (Math 1010) M / 11
20 Application - Demand Demand relates the price p of a service and the demand d at that price. This relationship may be linear. Set-up: From 2010, raffle tickets priced at $4 sold 2000 tickets. From 2011, raffle tickets priced at $5 sold 1800 tickets. Write a linear equation for the demand of tickets sold priced at p dollars. Use the equation to find the demand of tickets sold at $10 per ticket. (Math 1010) M / 11
21 Application - Demand Demand relates the price p of a service and the demand d at that price. This relationship may be linear. Set-up: From 2010, raffle tickets priced at $4 sold 2000 tickets. From 2011, raffle tickets priced at $5 sold 1800 tickets. Write a linear equation for the demand of tickets sold priced at p dollars. Use the equation to find the demand of tickets sold at $10 per ticket. Use the equation to find the demand of tickets sold at $2 per ticket. (Math 1010) M / 11
22 Assignment Assignment: For Wednesday: 1. Exercises from 3.4 due Wednesday, September Quiz # 3: Graphs, Linear Equations 3. Read section 3.6. (Skip 3.5) (Math 1010) M / 11
HFCC Math Lab Intermediate Algebra 1 SLOPE INTERCEPT AND POINT-SLOPE FORMS OF THE LINE
HFCC Math Lab Intermediate Algebra SLOPE INTERCEPT AND POINT-SLOPE FORMS OF THE LINE THE EQUATION OF A LINE Goal I. Use the slope-intercept form of the line to write the equation of a non-vertical line
Math 154 Elementary Algebra. Equations of Lines 4.4
Math Elementary Algebra Caspers Name Date Equations of Lines. For each graph, solve each equation for y (if necessary), then write down the slope and y-intercept.. y x. y x - - - - - - - - - - - - - -
3.5 Day 1 Warm Up. Graph each line. 3.4 Proofs with Perpendicular Lines
3.5 Day 1 Warm Up Graph each line. 1. y = 4x 2. y = 3x + 2 3. y = x 3 4. y = 4 x + 3 3 November 2, 2015 3.4 Proofs with Perpendicular Lines Geometry 3.5 Equations of Parallel and Perpendicular Lines Day
graphing_9.1.notebook March 15, 2019
1 2 3 Writing the equation of a line in slope intercept form. In order to write an equation in y = mx + b form you will need the slope "m" and the y intercept "b". We will subsitute the values for m and
slope rise run Definition of Slope
The Slope of a Line Mathematicians have developed a useful measure of the steepness of a line, called the slope of the line. Slope compares the vertical change (the rise) to the horizontal change (the
FLC Ch 3. Ex 1 Plot the points Ex 2 Give the coordinates of each point shown. Sec 3.2: Solutions and Graphs of Linear Equations
Math 100 Elementary Algebra Sec 3.1: The Rectangular Coordinate System x-axis and y-axis origin ordered pair x-coordinate y-coordinate quadrants (I, II, III, and IV) Rectangular/Cartesian Coordinate System
Math-2. Lesson 3-1. Equations of Lines
Math-2 Lesson 3-1 Equations of Lines How can an equation make a line? y = x + 1 x -4-3 -2-1 0 1 2 3 Fill in the rest of the table rule x + 1 f(x) -4 + 1-3 -3 + 1-2 -2 + 1-1 -1 + 1 0 0 + 1 1 1 + 1 2 2 +
Functions 3.6. Fall Math (Math 1010) M / 13
Functions 3.6 Fall 2013 - Math 1010 (Math 1010) M 1010 3.6 1 / 13 Roadmap 3.6 - Functions: Relations, Functions 3.6 - Evaluating Functions, Finding Domains and Ranges (Math 1010) M 1010 3.6 2 / 13 3.6
Forms of Linear Equations
6. 1-6.3 Forms of Linear Equations Name Sec 6.1 Writing Linear Equations in Slope-Intercept Form *Recall that slope intercept form looks like y = mx + b, where m = slope and b = y=intercept 1) Writing
Writing Linear Functions
2- Writing Linear Functions Objectives Use slope-intercept form and point-slope form to write linear functions. Write linear functions to solve problems. Vocabulary Point-slope form Why learn this? When
The Rectangular Coordinate System and Equations of Lines. College Algebra
The Rectangular Coordinate System and Equations of Lines College Algebra Cartesian Coordinate System A grid system based on a two-dimensional plane with perpendicular axes: horizontal axis is the x-axis
Graphing Linear Equations
Graphing Linear Equations A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. What am I learning today? How to graph a linear
Geometry Unit 2: Linear. Section Page and Problems Date Assigned
Geometry Name: Geometry Unit 2: Linear Topics Covered: Midpoint formula Distance formula Slope Slope- Intercept Form Point- Slope Form Standard Form Assignment # Section Page and Problems Date Assigned
Algebra 1 Semester 2 Final Review
Team Awesome 011 Name: Date: Period: Algebra 1 Semester Final Review 1. Given y mx b what does m represent? What does b represent?. What axis is generally used for x?. What axis is generally used for y?
Section Graphs and Lines
Section 1.1 - Graphs and Lines The first chapter of this text is a review of College Algebra skills that you will need as you move through the course. This is a review, so you should have some familiarity
Sec 4.1 Coordinates and Scatter Plots. Coordinate Plane: Formed by two real number lines that intersect at a right angle.
Algebra I Chapter 4 Notes Name Sec 4.1 Coordinates and Scatter Plots Coordinate Plane: Formed by two real number lines that intersect at a right angle. X-axis: The horizontal axis Y-axis: The vertical
List of Topics for Analytic Geometry Unit Test
List of Topics for Analytic Geometry Unit Test 1. Finding Slope 2. Rule of 4 (4 forms of a line) Graph, Table of Values, Description, Equation 3. Find the Equations- Vertical and Horizontal Lines 4. Standard
Math 1313 Prerequisites/Test 1 Review
Math 1313 Prerequisites/Test 1 Review Test 1 (Prerequisite Test) is the only exam that can be done from ANYWHERE online. Two attempts. See Online Assignments in your CASA account. Note the deadline too.
Tangent line problems
You will find lots of practice problems and homework problems that simply ask you to differentiate. The following examples are to illustrate some of the types of tangent line problems that you may come
Hot X: Algebra Exposed
Hot X: Algebra Exposed Solution Guide for Chapter 11 Here are the solutions for the Doing the Math exercises in Hot X: Algebra Exposed! DTM from p.149 2. Since m = 2, our equation will look like this:
Exploring Slope. We use the letter m to represent slope. It is the ratio of the rise to the run.
Math 7 Exploring Slope Slope measures the steepness of a line. If you take any two points on a line, the change in y (vertical change) is called the rise and the change in x (horizontal change) is called
Writing Equations of Lines and Midpoint
Writing Equations of Lines and Midpoint MGSE9 12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel
Relations and Functions 2.1
Relations and Functions 2.1 4 A 2 B D -5 5 E -2 C F -4 Relation a set of ordered pairs (Domain, Range). Mapping shows how each number of the domain is paired with each member of the range. Example 1 (2,
The Coordinate System and Graphs
The Coordinate System and Graphs - 3.1-3.2 Fall 2013 - Math 1010 (Math 1010) M 1010 3.1-3.2 1 / 17 Roadmap Plotting ordered pairs. The distance formula. The midpoint formula. Graphs of equations. Intercepts.
Classwork/Homework. Midterm Review. 1) 9 more than the product of a number and 12 2) 5 less than a number squared is twelve.
Name: Classwork/Homework Midterm Review Verbal Expressions *Translate the words to math * *The word THAN changes the order of the terms *Square Root, Cube Root 3 *Squared x 2, Cubed x 3 *Quantity use parentheses!
UNIT 4 NOTES. 4-1 and 4-2 Coordinate Plane
UNIT 4 NOTES 4-1 and 4-2 Coordinate Plane y Ordered pairs on a graph have several names. (X coordinate, Y coordinate) (Domain, Range) (Input,Output) Plot these points and label them: a. (3,-4) b. (-5,2)
Chapter 1 Section 1 Solving Linear Equations in One Variable
Chapter Section Solving Linear Equations in One Variable A linear equation in one variable is an equation which can be written in the form: ax + b = c for a, b, and c real numbers with a 0. Linear equations
Linear Functions. College Algebra
Linear Functions College Algebra Linear Function A linear function is a function whose graph is a straight line. Linear functions can be written in the slope-intercept form of a line: f(x) = mx + b where
Math Analysis Chapter 1 Notes: Functions and Graphs
Math Analysis Chapter 1 Notes: Functions and Graphs Day 6: Section 1-1 Graphs; Section 1- Basics of Functions and Their Graphs Points and Ordered Pairs The Rectangular Coordinate System (aka: The Cartesian
Sketching Straight Lines (Linear Relationships)
Sketching Straight Lines (Linear Relationships) The slope of the line is m = y x = y 2 y 1 = rise run. Horizontal lines have the form y = b and have slope m = 0. Vertical lines have the form x = a and
Summer Math Assignments for Students Entering Algebra II
Summer Math Assignments for Students Entering Algebra II Purpose: The purpose of this packet is to review pre-requisite skills necessary for the student to be successful in Algebra II. You are expected
SLOPE A MEASURE OF STEEPNESS through 7.1.5
SLOPE A MEASURE OF STEEPNESS 7.1. through 7.1.5 Students have used the equation = m + b throughout this course to graph lines and describe patterns. When the equation is written in -form, the m is the
Intro. To Graphing Linear Equations
Intro. To Graphing Linear Equations The Coordinate Plane A. The coordinate plane has 4 quadrants. B. Each point in the coordinate plain has an x-coordinate (the abscissa) and a y-coordinate (the ordinate).
10-2 Circles. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra2 2
10-2 Circles Warm Up Lesson Presentation Lesson Quiz Holt Algebra2 2 Warm Up Find the slope of the line that connects each pair of points. 1. (5, 7) and ( 1, 6) 1 6 2. (3, 4) and ( 4, 3) 1 Warm Up Find
Writing and Graphing Linear Equations. Linear equations can be used to represent relationships.
Writing and Graphing Linear Equations Linear equations can be used to represent relationships. Linear equation An equation whose solutions form a straight line on a coordinate plane. Collinear Points that
In math, the rate of change is called the slope and is often described by the ratio rise
Chapter 3 Equations of Lines Sec. Slope The idea of slope is used quite often in our lives, however outside of school, it goes by different names. People involved in home construction might talk about
Lesson 20: Every Line is a Graph of a Linear Equation
Student Outcomes Students know that any non vertical line is the graph of a linear equation in the form of, where is a constant. Students write the equation that represents the graph of a line. Lesson
The shortest distance from point K to line is the length of a segment perpendicular to from point K. Draw a perpendicular segment from K to.
8. Find the distance between each pair of parallel lines with the given equations. Copy each figure. Construct the segment that represents the distance indicated. 12. K to The shortest distance from point
You should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1
Name GRAPHICAL REPRESENTATION OF DATA: You should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1 ) and (x, y ) is x1 x y1 y,.
Section 2.2 Graphs of Linear Functions
Section. Graphs of Linear Functions Section. Graphs of Linear Functions When we are working with a new function, it is useful to know as much as we can about the function: its graph, where the function
Linear Equations in Two Variables
Section. Linear Equations in Two Variables Section. Linear Equations in Two Variables You should know the following important facts about lines. The graph of b is a straight line. It is called a linear
Summer Math Assignments for Students Entering Integrated Math
Summer Math Assignments for Students Entering Integrated Math Purpose: The purpose of this packet is to review pre-requisite skills necessary for the student to be successful in Integrated Math. You are
GEOMETRY APPLICATIONS
GEOMETRY APPLICATIONS Chapter 3: Parallel & Perpendicular Lines Name: Teacher: Pd: 0 Table of Contents DAY 1: (Ch. 3-1 & 3-2) SWBAT: Identify parallel, perpendicular, and skew lines. Identify the angles
JUST THE MATHS SLIDES NUMBER 5.2. GEOMETRY 2 (The straight line) A.J.Hobson
JUST THE MATHS SLIDES NUMBER 5.2 GEOMETRY 2 (The straight line) by A.J.Hobson 5.2.1 Preamble 5.2.2 Standard equations of a straight line 5.2.3 Perpendicular straight lines 5.2.4 Change of origin UNIT 5.2
CHAPTER 2 REVIEW COORDINATE GEOMETRY MATH Warm-Up: See Solved Homework questions. 2.2 Cartesian coordinate system
CHAPTER 2 REVIEW COORDINATE GEOMETRY MATH6 2.1 Warm-Up: See Solved Homework questions 2.2 Cartesian coordinate system Coordinate axes: Two perpendicular lines that intersect at the origin O on each line.
Writing Equations of Parallel and Perpendicular Lines
Writing Equations of Parallel and Perpendicular Lines The coordinate plane provides a connection between algebra and geometry. Postulates 17 and 18 establish a simple way to find lines that are parallel
College Prep Algebra II Summer Packet
Name: College Prep Algebra II Summer Packet This packet is an optional review which is highly recommended before entering CP Algebra II. It provides practice for necessary Algebra I topics. Remember: When
MATH 021 UNIT 2 HOMEWORK ASSIGNMENTS
MATH 021 UNIT 2 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usually, the part (A) questions ask for explanations,
3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up. Consider the equation y x.
3.1 Start Thinking Consider the equation y x. Are there any values of x that you cannot substitute into the equation? If so, what are they? Are there any values of y that you cannot obtain as an answer?
Chapter 1. Linear Equations and Straight Lines. 2 of 71. Copyright 2014, 2010, 2007 Pearson Education, Inc.
Chapter 1 Linear Equations and Straight Lines 2 of 71 Outline 1.1 Coordinate Systems and Graphs 1.4 The Slope of a Straight Line 1.3 The Intersection Point of a Pair of Lines 1.2 Linear Inequalities 1.5
Algebra I Notes Linear Equations and Inequalities in Two Variables Unit 04c
Big Idea: Describe the similarities and differences between equations and inequalities including solutions and graphs. Skill: graph linear equations and find possible solutions to those equations using
^ebmi^h4^e^tu ^ <J -f^e tcne pusn\$ &nw$k M^^at [-2>\ ij»4j \
![^ebmi^h4^e^tu ^ <J -f^e tcne pusn\$ &nw$k M^^at [-2>\ ij»4j \](/thumbs/74/71020934.jpg "^ebmi^h4^e^tu ^ <J -f^e tcne pusn\$ &nw$k M^^at [-2>\ ij»4j \")
^ebmi^h4^e^tu ^ \ ij»4j \ febrw -kf epufta. (X^ kite p*v»jfe/ ^ # 1 pusrv^ -fafk&kt Mepci't\{r & kjc*f*«t -He t^ih^ (ft fte.^ ^peraiujs*- -fwifv^k point 1 \ 7. 3 (o)
GEOMETRY HONORS COORDINATE GEOMETRY PACKET
GEOMETRY HONORS COORDINATE GEOMETRY PACKET Name Period Homework Lesson Assignment Day 1 - Slopes of Perpendicular WKSHT and Parallel Lines Day 2 - Writing an Equation of a Line HW- Honors TXTBK pages 615-617
Algebra I Notes Unit Six: Graphing Linear Equations and Inequalities in Two Variables, Absolute Value Functions
Sllabus Objective.4 The student will graph linear equations and find possible solutions to those equations using coordinate geometr. Coordinate Plane a plane formed b two real number lines (axes) that
Final Exam MAT 100 JS 2018
Final Exam MAT 100 JS 2018 Miles College T Dabit MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell which set or sets the number belongs to: natural
Mathematics (www.tiwariacademy.com)
() Miscellaneous Exercise on Chapter 10 Question 1: Find the values of k for which the line is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin. Answer 1: The given
2.1. Rectangular Coordinates and Graphs. 2.1 Rectangular Coordinates and Graphs 2.2 Circles 2.3 Functions 2.4 Linear Functions. Graphs and Functions
2 Graphs and Functions 2 Graphs and Functions 2.1 Rectangular Coordinates and Graphs 2.2 Circles 2.3 Functions 2.4 Linear Functions Sections 2.1 2.4 2008 Pearson Addison-Wesley. All rights reserved Copyright
Name Date. Modeling with Linear Functions For use with Exploration 1.3
1.3 Modeling with Linear Functions For use with Exploration 1.3 Essential Question How can ou use a linear function to model and analze a real-life situation? 1 EXPLORATION: Modeling with a Linear Function
Practice Test (page 391) 1. For each line, count squares on the grid to determine the rise and the run. Use slope = rise
Practice Test (page 91) 1. For each line, count squares on the grid to determine the rise and the. Use slope = rise 4 Slope of AB =, or 6 Slope of CD = 6 9, or Slope of EF = 6, or 4 Slope of GH = 6 4,
Did You Find a Parking Space?
Lesson.4 Skills Practice Name Date Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane Vocabulary Complete the sentence. 1. The point-slope form of the equation of the
Algebra. Chapter 5: LINEAR FUNCTIONS. Name: Teacher: Pd:
Algebra Chapter 5: LINEAR FUNCTIONS Name: Teacher: Pd: Day 1 - Chapter 5-3/5-4: Slope SWBAT: Calculate the slope from any two points Pgs. #1-5 Hw pgs. #6 7 Table of Contents Day 2 - Chapter 5-6: Slope
MATH 099 HOMEWORK TWO
MATH 099 HOMEWORK TWO STUDENT S NAME 1) Matthew needs to rent a car for 1 day. He will be charged a daily fee of $30.00 in addition to 5 cents for every mile he drives. Assign the variable by letting x
2.1 Solutions to Exercises
Last edited 9/6/17.1 Solutions to Exercises 1. P(t) = 1700t + 45,000. D(t) = t + 10 5. Timmy will have the amount A(n) given by the linear equation A(n) = 40 n. 7. From the equation, we see that the slope
Vertical Line Test a relationship is a function, if NO vertical line intersects the graph more than once
Algebra 2 Chapter 2 Domain input values, X (x, y) Range output values, Y (x, y) Function For each input, there is exactly one output Example: Vertical Line Test a relationship is a function, if NO vertical
UNIT NUMBER 5.2. GEOMETRY 2 (The straight line) A.J.Hobson
JUST THE MATHS UNIT NUMBER 5.2 GEOMETRY 2 (The straight line) b A.J.Hobson 5.2.1 Preamble 5.2.2 Standard equations of a straight line 5.2. Perpendicular straight lines 5.2.4 Change of origin 5.2.5 Exercises
Section 3.1 Objective 1: Plot Points in the Rectangular Coordinate System Video Length 12:35
Section 3.1 Video Guide The Rectangular Coordinate System and Equations in Two Variables Objectives: 1. Plot Points in the Rectangular Coordinate System 2. Determine If an Ordered Pair Satisfies an Equation
Math 101 Exam 1 Review
Math 101 Exam 1 Review Reminder: Exam 1 will be on Friday, October 14, 011 at 8am. It will cover sections 1.1, 1. and 10.1 10.3 Room Assignments: Room Sections Nesbitt 111 9, 14, 3, 4, 8 Nesbitt 15 0,
Math Analysis Chapter 1 Notes: Functions and Graphs
Math Analysis Chapter 1 Notes: Functions and Graphs Day 6: Section 1-1 Graphs Points and Ordered Pairs The Rectangular Coordinate System (aka: The Cartesian coordinate system) Practice: Label each on the
Algebra II Notes Unit Two: Linear Equations and Functions
Syllabus Objectives:.1 The student will differentiate between a relation and a function.. The student will identify the domain and range of a relation or function.. The student will derive a function rule
WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING)
WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING) 1 Contents Some Simple Straight Lines y = mx + c Parallel Lines Perpendicular Lines Plotting Equations Shaded Regions Credits WJEC Question
Name: NOTES 5: LINEAR EQUATIONS AND THEIR GRAPHS. Date: Period: Mrs. Nguyen s Initial: LESSON 5.1 RATE OF CHANGE AND SLOPE. A. Finding rates of change
NOTES : LINEAR EQUATIONS AND THEIR GRAPHS Name: Date: Period: Mrs. Nguen s Initial: LESSON. RATE OF CHANGE AND SLOPE A. Finding rates of change vertical change Rate of change = = change in x The rate of
Linear Modeling Elementary Education 4
Linear Modeling Elementary Education 4 Mathematical modeling is simply the act of building a model (usually in the form of graphs) which provides a picture of a numerical situation. Linear Modeling is
Name: Hour: Algebra. Unit 2. Booklet
Name: Hour: Algebra Unit 2 Booklet Finding Slope on a Graph 1 2 3 4 Finding Slope from points 1 2 3 4 1 VERTICAL LINE Equation: Slope: Horizontal and Vertical Lines Equation: Slope: HORIZONTAL LINE 2 Forms
2. Write the point-slope form of the equation of the line passing through the point ( 2, 4) with a slope of 3. (1 point)
Parallel and Perpendicular Lines Unit Test David Strong is taking this assessment. Multiple Choice 1. Which construction is illustrated above? a segment congruent to a given segment an angle congruent
Please do NOT use a calculator unless problem is marked with an asterisk. (*) SHOW work for all problems, including calculator-permitted ones!
Please do NOT use a calculator unless problem is marked with an asterisk. (*) ASMT 31: see Oct 2018 Calendar (on Weebly) for due dates Review Les 3.7 3.8; Study for QUIZ 4 Wednesday (over Les 3.3 3.7)
Lesson 19: The Graph of a Linear Equation in Two Variables is a Line
Lesson 19: The Graph of a Linear Equation in Two Variables is a Line Classwork Exercises Theorem: The graph of a linear equation y = mx + b is a non-vertical line with slope m and passing through (0, b),
Section 1.1 The Distance and Midpoint Formulas
Section 1.1 The Distance and Midpoint Formulas 1 y axis origin x axis 2 Plot the points: ( 3, 5), (0,7), ( 6,0), (6,4) 3 Distance Formula y x 4 Finding the Distance Between Two Points Find the distance
LINEAR TOPICS Notes and Homework: DUE ON EXAM
NAME CLASS PERIOD LINEAR TOPICS Notes and Homework: DUE ON EXAM VOCABULARY: Make sure ou know the definitions of the terms listed below. These will be covered on the exam. Axis Scatter plot b Slope Coordinate
AP Calculus Summer Review Packet
AP Calculus Summer Review Packet Name: Date began: Completed: **A Formula Sheet has been stapled to the back for your convenience!** Email anytime with questions: danna.seigle@henry.k1.ga.us Complex Fractions
SNAP Centre Workshop. Graphing Lines
SNAP Centre Workshop Graphing Lines 45 Graphing a Line Using Test Values A simple way to linear equation involves finding test values, plotting the points on a coordinate plane, and connecting the points.
Unit 1: Module 1 Quantitative Reasoning. Unit 1: Module 2 Algebraic Models. Unit 2: Module 3 Functions and Models. Unit 3: Module 5 Linear Functions
Fall Unit : Module Quantitative Reasoning Unit : Module 2 Algebraic Models Unit 2: Module 3 and Models Unit 3: Module 5 Linear Unit 3: Module 6 Forms of Linear Equations Unit 5: Module Solving Systems
Review for Mastery Using Graphs and Tables to Solve Linear Systems
3-1 Using Graphs and Tables to Solve Linear Systems A linear system of equations is a set of two or more linear equations. To solve a linear system, find all the ordered pairs (x, y) that make both equations
5.1 Introduction to the Graphs of Polynomials
Math 3201 5.1 Introduction to the Graphs of Polynomials In Math 1201/2201, we examined three types of polynomial functions: Constant Function - horizontal line such as y = 2 Linear Function - sloped line,
3-6 Lines in the Coordinate Plane
3-6 Lines in the Coordinate Plane Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and
Intensive Math-Algebra I Mini Lesson MA.912.A.3.10
Intensive Math-Algebra I Mini Lesson M912.3.10 Summer 2013 Writing Equations of Perpendicular Lines Student Packet Day 10 Name: Date: Benchmark M912.3.10 Write an equation of a line given any of the following
Important!!! First homework is due on Monday, September 26 at 8:00 am.
Important!!! First homework is due on Monday, September 26 at 8:00 am. You can solve and submit the homework on line using webwork: http://webwork.dartmouth.edu/webwork2/m3cod/. If you do not have a user
2-5 Graphing Special Functions. Graph each function. Identify the domain and range. SOLUTION:
Graph each function Identify the domain and range Write the piecewise-defined function shown in each graph 1 3 The left portion of the graph is the line g(x) = x + 4 There is an open circle at ( 2, 2),
Area of triangle? Area of square? Area of Rectangle? distance formula: slope point form: slope intercept form: February 22, 2017
Formula Page for this Unit! Quiz tomorrow! Slope Formula: rise run slope intercept form: slope point form: distance formula: Area of triangle? Area of parallelogram? Area of square? Area of Rectangle?
CHAPTER 5: LINEAR EQUATIONS AND THEIR GRAPHS Notes#26: Section 5-1: Rate of Change and Slope
Name: Date: Period: CHAPTER : LINEAR EQUATIONS AND THEIR GRAPHS Notes#: Section -: Rate of Change and Slope A. Finding rates of change vertical change Rate of change change in x The rate of change is constant
Graphing Linear Equations
Graphing Linear Equations Question 1: What is a rectangular coordinate system? Answer 1: The rectangular coordinate system is used to graph points and equations. To create the rectangular coordinate system,
Derivatives. Day 8 - Tangents and Linearizations
Derivatives Day 8 - Tangents and Linearizations Learning Objectives Write an equation for the tangent line to a graph Write an equation for the normal line to a graph Find the locations of horizontal and
AP Statistics Summer Review Packet
60 NAME: PERIOD: AP Statistics Summer Review Packet Teacher(s): Ryan Oben Teacher(s) Contact Information: Ryan_Oben@mcpsmd.org Course: Purpose of the Summer Assignment: In general, AP Statistics includes
NO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED
Algebra II (Wilsen) Midterm Review NO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED Remember: Though the problems in this packet are a good representation of many of the topics that will be on the exam, this
Study Guide for Exam 2
Math 233A Intermediate Algebra Fall 202 Study Guide for Exam 2 Exam 2 is scheduled for Wednesday, October 3 rd. You may use a 3" 5" note card (both sides) and a scientific calculator. You are expected
Chapter 11 GRAPHS OF LINEAR EQUATIONS
Chapter 11 GRAPHS OF LINEAR EQUATIONS 11.1 Graphs and Applications of Linear Equations Learning Objectives A Plot points associated with ordered pairs of numbers; determine the quadrant in which a point
School Year:
School Year: 2010 2011 1 McDougal Littell CA Math Algebra 1 Pacing Guide Begin First Semester During the first two weeks of school, teachers will work with students on study skills and diagnostic assessments
Geometry Unit 5 Geometric and Algebraic Connections. Table of Contents
Geometry Unit 5 Geometric and Algebraic Connections Table of Contents Lesson 5 1 Lesson 5 2 Distance.p. 2-3 Midpoint p. 3-4 Partitioning a Directed Line. p. 5-6 Slope. p.7-8 Lesson 5 3 Revisit: Graphing
Unit 6: Connecting Algebra and Geometry Through Coordinates
Unit 6: Connecting Algebra and Geometry Through Coordinates The focus of this unit is to have students analyze and prove geometric properties by applying algebraic concepts and skills on a coordinate plane.
Slide 1 / 220. Linear Relations and Functions
Slide 1 / 220 Linear Relations and Functions Slide 2 / 220 Table of Contents Domain and Range Discrete v Continuous Relations and Functions Function Notation Linear Equations Graphing a Linear Equation
1. Answer: x or x. Explanation Set up the two equations, then solve each equation. x. Check
Thinkwell s Placement Test 5 Answer Key If you answered 7 or more Test 5 questions correctly, we recommend Thinkwell's Algebra. If you answered fewer than 7 Test 5 questions correctly, we recommend Thinkwell's