Lesson 19: The Graph of a Linear Equation in Two Variables Is a Line
|
|
|
- Darren Maxwell
- 5 years ago
- Views:
Transcription
1 The Graph of a Linear Equation in Two Variables Is a Line Classwork Exercises THEOREM: The graph of a linear equation yy = mmmm + bb is a non-vertical line with slope mm and passing through (0, bb), where bb is a constant. 1. Prove the theorem by completing parts (a) (c). Given two distinct points, PP and QQ, on the graph of yy = mmmm + bb, and let ll be the line passing through PP and QQ. You must show the following: (1) Any point on the graph of yy = mmmm + bb is on line ll, and (2) Any point on the line ll is on the graph of yy = mmmm + bb. a. Proof of (1): Let RR be any point on the graph of yy = mmmm + bb. Show that RR is on ll. Begin by assuming it is not. Assume the graph looks like the diagram below where RR is on ll. What is the slope of line ll? S.108
2 What is the slope of line ll? What can you conclude about lines ll and ll? Explain. b. Proof of (2): Let SS be any point on line ll, as shown. Show that SS is a solution to yy = mmmm + bb. Hint: Use the point (0, bb). S.109
3 c. Now that you have shown that any point on the graph of yy = mmmm + bb is on line ll in part (a), and any point on line ll is on the graph of yy = mmmm + bb in part (b), what can you conclude about the graphs of linear equations? 2. Use mm = 4 and mm = 4 to find two solutions to the equation mm + 2yy = 6. Plot the solutions as points on the coordinate plane, and connect the points to make a line. a. Identify two other points on the line with integer coordinates. Verify that they are solutions to the equation mm + 2yy = 6. b. When mm = 1, what is the value of yy? Does this solution appear to be a point on the line? c. When mm = 3, what is the value of yy? Does this solution appear to be a point on the line? d. Is the point (3, 2) on the line? e. Is the point (3, 2) a solution to the linear equation mm + 2yy = 6? S.110
4 3. Use mm = 4 and mm = 1 to find two solutions to the equation 3mm yy = 9. Plot the solutions as points on the coordinate plane, and connect the points to make a line. a. Identify two other points on the line with integer coordinates. Verify that they are solutions to the equation 3mm yy = 9. b. When mm = 4.5, what is the value of yy? Does this solution appear to be a point on the line? c. When mm = 1, what is the value of yy? Does this solution appear to be a point on the line? 2 d. Is the point (2, 4) on the line? e. Is the point (2, 4) a solution to the linear equation 3mm yy = 9? 4. Use mm = 3 and mm = 3 to find two solutions to the equation 2mm + 3yy = 12. Plot the solutions as points on the coordinate plane, and connect the points to make a line. a. Identify two other points on the line with integer coordinates. Verify that they are solutions to the equation 2mm + 3yy = 12. S.111
5 b. When mm = 2, what is the value of yy? Does this solution appear to be a point on the line? c. When mm = 2, what is the value of yy? Does this solution appear to be a point on the line? d. Is the point (8, 3) on the line? e. Is the point (8, 3) a solution to the linear equation 2mm + 3yy = 12? 5. Use mm = 4 and mm = 4 to find two solutions to the equation mm 2yy = 8. Plot the solutions as points on the coordinate plane, and connect the points to make a line. a. Identify two other points on the line with integer coordinates. Verify that they are solutions to the equation mm 2yy = 8. b. When mm = 7, what is the value of yy? Does this solution appear to be a point on the line? S.112
6 c. When mm = 3, what is the value of yy? Does this solution appear to be a point on the line? d. Is the point ( 2, 3) on the line? e. Is the point ( 2, 3) a solution to the linear equation mm 2yy = 8? 6. Based on your work in Exercises 2 5, what conclusions can you draw about the points on a line and solutions to a linear equation? 7. Based on your work in Exercises 2 5, will a point that is not a solution to a linear equation be a point on the graph of a linear equation? Explain. 8. Based on your work in Exercises 2 5, what conclusions can you draw about the graph of a linear equation? S.113
7 9. Graph the equation 3mm + 8yy = 24 using intercepts. 10. Graph the equation mm 6yy = 15 using intercepts. 11. Graph the equation 4mm + 3yy = 21 using intercepts. S.114
8 Lesson Summary The graph of a linear equation is a line. A linear equation can be graphed using two-points: the mm-intercept point and the yy-intercept point. Example: Graph the equation: 2mm + 3yy = 9. Replace mm with zero, and solve for yy to determine the yy-intercept point. The yy-intercept point is at (0, 3). 2(0) + 3yy = 9 3yy = 9 yy = 3 Replace yy with zero, and solve for mm to determine the mm-intercept point. 2mm + 3(0) = 9 2mm = 9 mm = 9 2 The mm-intercept point is at ( 9 2, 0). S.115
9 Problem Set Graph each of the equations in the Problem Set on a different pair of mm- and yy-axes. 1. Graph the equation: yy = 6mm Graph the equation: 9mm + 3yy = Graph the equation: yy = 4mm Graph the equation: yy = 5 mm Graph the equation: 3 mm + yy = Graph the equation: 2mm 4yy = Graph the equation: yy = 3. What is the slope of the graph of this line? 8. Graph the equation: mm = 4. What is the slope of the graph of this line? 9. Is the graph of 4mm + 5yy = 3 a line? Explain Is the graph of 6mm 2 2yy = 7 a line? Explain. S.116
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),
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
Lesson 18: There is Only One Line Passing Through a Given Point with a Given
Lesson 18: There is Only One Line Passing Through a Given Point with a Given Student Outcomes Students graph equations in the form of using information about slope and intercept. Students know that if
Lesson 12: Angles Associated with Parallel Lines
Lesson 12 Lesson 12: Angles Associated with Parallel Lines Classwork Exploratory Challenge 1 In the figure below, LL 1 is not parallel to LL 2, and mm is a transversal. Use a protractor to measure angles
Grade 8 Mathematics Item Specification C1 TC
Task Model 1 Graphing DOK Level 1, interpreting the unit rate as the slope of the graph. Compare two different example, compare a distance-time graph to a distance-time two moving objects has greater speed.
Lesson 14: Graph of a Linear Equation Horizontal and Vertical Lines
Lesson 14: Graph of a Linear Equation Horizontal and Vertical Lines Student Outcomes Students graph linear equations in standard form, 0), that produce a horizontal or a vertical line. Lesson Notes The
Functions. Name. Use an XY Coordinate Pegboard to graph each line. Make a table of ordered pairs for each line. y = x + 5 x y.
Lesson 1 Functions Name Use an XY Coordinate Pegboard to graph each line. Make a table of ordered pairs for each line. 1. = + = + = 2 3 = 2 3 Using an XY Coordinate Pegboard, graph the line on a coordinate
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
Lesson 24: Matrix Notation Encompasses New Transformations!
Classwork Example 1 Determine the following: a. 1 0 0 1 3 b. 1 0 7 0 1 1 c. 1 0 3 5 0 1 1 d. 1 0 3 1 0 1 7 6 e. 9 1 0 1 3 1 0 1 f. 1 0 cc aa 0 1 bb dd xx yy 0 g. 1 zz ww 0 1 Date: 1/5/15 S.14 Example Can
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.
Notes Lesson 3 4. Positive. Coordinate. lines in the plane can be written in standard form. Horizontal
A, B, C are Notes Lesson 3 4 Standard Form of an Equation: Integers Ax + By = C Sometimes it is preferred that A is Positive All lines in the plane can be written in standard form. Oblique Coordinate Horizontal
2.1 Transforming Linear Functions
2.1 Transforming Linear Functions Before we begin looking at transforming linear functions, let s take a moment to review how to graph linear equations using slope intercept form. This will help us because
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?
Lesson 6. Opening Exercise 1. Without graphing, state the vertex for each of the following quadratic equations.
: Further Exploration of Vertex Form, yy = aa(xx hh) + kk Opening Exercise 1. Without graphing, state the vertex for each of the following quadratic equations. A. yy = (xx 5) + 3 B. yy = xx.5 C. yy = (xx
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
Lesson 1: Why Move Things Around?
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 8 2 Lesson 1: Why Move Things Around? Classwork Exploratory Challenge a Describe, intuitively, what kind of transformation is required to move the figure
Lesson 5: Graphs of Functions and Equations
Classwork Exploratory Challenge/Exercises 1 3 1. The distance that Giselle can run is a function of the amount of time she spends running. Giselle runs 3 miles in 21 minutes. Assume she runs at a constant
Unit 3 Notes: Parallel Lines, Perpendicular Lines, and Angles 3-1 Transversal
Unit 3 Notes: Parallel Lines, Perpendicular Lines, and Angles 3-1 Transversal REVIEW: *Postulates are Fundamentals of Geometry (Basic Rules) To mark line segments as congruent draw the same amount of tic
This is called the vertex form of the quadratic equation. To graph the equation
Name Period Date: Topic: 7-5 Graphing ( ) Essential Question: What is the vertex of a parabola, and what is its axis of symmetry? Standard: F-IF.7a Objective: Graph linear and quadratic functions and show
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
Lesson 13: The Graph of a Linear Equation in Two Variables
Student Outcomes Students predict the shape of a graph of a linear equation by finding and plotting solutions on a coordinate plane. Students informally explain why the graph of a linear equation is not
.(3, 2) Co-ordinate Geometry Co-ordinates. Every point has two co-ordinates. Plot the following points on the plane. A (4, 1) D (2, 5) G (6, 3)
Co-ordinate Geometry Co-ordinates Every point has two co-ordinates. (3, 2) x co-ordinate y co-ordinate Plot the following points on the plane..(3, 2) A (4, 1) D (2, 5) G (6, 3) B (3, 3) E ( 4, 4) H (6,
Lesson 12: The Graph of the Equation y = f(x)
Classwork In Module 1, you graphed equations such as 4x + y = 10 by plotting the points on the Cartesian coordinate plane that corresponded to all of the ordered pairs of numbers (x, y) that were in the
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 +
Eureka Math. Geometry, Module 4. Student File_B. Contains Exit Ticket, and Assessment Materials
A Story of Functions Eureka Math Geometry, Module 4 Student File_B Contains Exit Ticket, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work
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
WHAT YOU SHOULD LEARN
GRAPHS OF EQUATIONS WHAT YOU SHOULD LEARN Sketch graphs of equations. Find x- and y-intercepts of graphs of equations. Use symmetry to sketch graphs of equations. Find equations of and sketch graphs of
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
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
Lattice Polygon s and Pick s Theorem From Dana Paquin and Tom Davis 1 Warm-Up to Ponder
Lattice Polygon s and Pick s Theorem From Dana Paquin and Tom Davis http://www.geometer.org/mathcircles/pick.pdf 1 Warm-Up to Ponder 1. Is it possible to draw an equilateral triangle on graph paper so
Pick s Theorem and Lattice Point Geometry
Pick s Theorem and Lattice Point Geometry 1 Lattice Polygon Area Calculations Lattice points are points with integer coordinates in the x, y-plane. A lattice line segment is a line segment that has 2 distinct
Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets
Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of the way along each median
Lesson 19: Translating Functions
Student Outcomes Students recognize and use parent functions for linear, absolute value, quadratic, square root, and cube root functions to perform vertical and horizontal translations. They identify how
Lesson 3: Solving for Unknown Angles using Equations
Classwork Opening Exercise Two lines meet at the common vertex of two rays; the measurement of. Set up and solve an equation to find the value of and. Example 1 Set up and solve an equation to find the
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
Section Graphs of the Sine and Cosine Functions
Section 5. - Graphs of the Sine and Cosine Functions In this section, we will graph the basic sine function and the basic cosine function and then graph other sine and cosine functions using transformations.
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
Visit MathNation.com or search "Math Nation" in your phone or tablet's app store to watch the videos that go along with this workbook!
Topic 1: Introduction to Angles - Part 1... 47 Topic 2: Introduction to Angles Part 2... 50 Topic 3: Angle Pairs Part 1... 53 Topic 4: Angle Pairs Part 2... 56 Topic 5: Special Types of Angle Pairs Formed
5 and Parallel and Perpendicular Lines
Ch 3: Parallel and Perpendicular Lines 3 1 Properties of Parallel Lines 3 Proving Lines Parallel 3 3 Parallel and Perpendicular Lines 3 Parallel Lines and the Triangle Angles Sum Theorem 3 5 The Polgon
Graphs and Linear Functions
Graphs and Linear Functions A -dimensional graph is a visual representation of a relationship between two variables given by an equation or an inequality. Graphs help us solve algebraic problems by analysing
Lesson 3 Practice Problems
Name: Date: Lesson 3 Section 3.1: Linear Equations and Functions 1. Find the slope of the line that passes through the given points. Then determine if the line is increasing, decreasing or constant. Increasing,
Hot X: Algebra Exposed
Hot X: Algebra Exposed Solution Guide for Chapter 10 Here are the solutions for the Doing the Math exercises in Hot X: Algebra Exposed! DTM from p.137-138 2. To see if the point is on the line, let s plug
f( x ), or a solution to the equation f( x) 0. You are already familiar with ways of solving
The Bisection Method and Newton s Method. If f( x ) a function, then a number r for which f( r) 0 is called a zero or a root of the function f( x ), or a solution to the equation f( x) 0. You are already
Lesson 13: Angle Sum of a Triangle
Student Outcomes Students know the Angle Sum Theorem for triangles; the sum of the interior angles of a triangle is always 180. Students present informal arguments to draw conclusions about the angle sum
Lesson 13: Exploring Factored Form
Opening Activity Below is a graph of the equation y = 6(x 3)(x + 2). It is also the graph of: y = 3(2x 6)(x + 2) y = 2(3x 9)(x + 2) y = 2(x 3)(3x + 6) y = 3(x 3)(2x + 4) y = (3x 9)(2x + 4) y = (2x 6)(3x
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,
Lesson 20: Four Interesting Transformations of Functions
Student Outcomes Students apply their understanding of transformations of functions and their graphs to piecewise functions. Lesson Notes In Lessons 17 19 students study translations and scalings of functions
Polynomial Functions I
Name Student ID Number Group Name Group Members Polnomial Functions I 1. Sketch mm() =, nn() = 3, ss() =, and tt() = 5 on the set of aes below. Label each function on the graph. 15 5 3 1 1 3 5 15 Defn:
Lesson 14: A Closer Look at Linear & Exponential Functions
Opening Exercise Linear versus Exponential Functions Let s look at the difference between ff(nn) = 2nn and ff(nn) = 2 nn.. Complete the tables below, and then graph the points nn, ff(nn) on a coordinate
UNIT 4 DESCRIPTIVE STATISTICS Lesson 2: Working with Two Categorical and Quantitative Variables Instruction
Prerequisite Skills This lesson requires the use of the following skills: plotting points on the coordinate plane, given data in a table plotting the graph of a linear function, given an equation plotting
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
2 and 6 4 and 8 1 and 5 3 and 7
Geo Ch 3 Angles formed by Lines Parallel lines are two coplanar lines that do not intersect. Skew lines are that are not coplanar and do not intersect. Transversal is a line that two or more lines at different
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
TECHNISCHE UNIVERSITÄT BERLIN WS2005 Fachbereich 3 - Mathematik Prof. Dr. U. Pinkall / Charles Gunn Abgabe:
TECHNISCHE UNIVERSITÄT BERLIN WS2005 Fachbereich 3 - Mathematik Prof. Dr. U. Pinkall / Charles Gunn Abgabe: 27.10.2005 1. Übung Geometrie I (Lines in P 2 (R), Separation, Desargues) 1. Aufgabe Line equations
Warmup pg. 137 #1-8 in the geo book 6 minutes to finish
Chapter Three Test Friday 2/2 Warmup pg. 137 #1-8 in the geo book 6 minutes to finish 1 1 and 5, 2 and 5 3 and 4 1 and 2 1 and 5, 2 and 5 division prop of eq Transitive prop of congruency 16 = 4x x = 4
Graphs of Equations. MATH 160, Precalculus. J. Robert Buchanan. Fall Department of Mathematics. J. Robert Buchanan Graphs of Equations
Graphs of Equations MATH 160, Precalculus J. Robert Buchanan Department of Mathematics Fall 2011 Objectives In this lesson we will learn to: sketch the graphs of equations, find the x- and y-intercepts
Have students complete the summary table, and then share as a class to make sure students understand concepts.
Closing (5 minutes) Have students complete the summary table, and then share as a class to make sure students understand concepts. Lesson Summary: We have just developed proofs for an entire family of
Warm-Up Exercises. Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; y = 2x + 7 ANSWER ; 7
Warm-Up Exercises Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; 3 2. y = 2x + 7 7 2 ANSWER ; 7 Chapter 1.1 Graph Quadratic Functions in Standard Form A quadratic function is a function that
Chapter 10. Homework
Chapter 0 Homework Lesson 0- pages 538 5 Exercises. 2. Hyperbola: center (0, 0), y-intercepts at ±, no x-intercepts, the lines of symmetry are the x- and y-axes; domain: all real numbers, range: y 5 3
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,
Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means
: Analytic Proofs of Theorems Previously Proved by Synthetic Means Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of
Meeting 1 Introduction to Functions. Part 1 Graphing Points on a Plane (REVIEW) Part 2 What is a function?
Meeting 1 Introduction to Functions Part 1 Graphing Points on a Plane (REVIEW) A plane is a flat, two-dimensional surface. We describe particular locations, or points, on a plane relative to two number
Module Four: Connecting Algebra and Geometry Through Coordinates
NAME: Period: Module Four: Connecting Algebra and Geometry Through Coordinates Topic A: Rectangular and Triangular Regions Defined by Inequalities Lesson 1: Searching a Region in the Plane Lesson 2: Finding
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
CCGPS UNIT 5 Semester 2 COORDINATE ALGEBRA Page 1 of 38. Transformations in the Coordinate Plane
CCGPS UNIT 5 Semester 2 COORDINATE ALGEBRA Page 1 of 38 Transformations in the Coordinate Plane Name: Date: MCC9-12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line,
Lesson 7. Opening Exercise Warm Up 1. Without graphing, state the vertex for each of the following quadratic equations.
: Further Explorations of Vertex Form, yy = aa(xx hh) + kk Opening Exercise Warm Up 1. Without graphing, state the vertex for each of the following quadratic equations. A. yy = (xx 5) + 3 B. yy = xx.5
To sketch the graph we need to evaluate the parameter t within the given interval to create our x and y values.
Module 10 lesson 6 Parametric Equations. When modeling the path of an object, it is useful to use equations called Parametric equations. Instead of using one equation with two variables, we will use two
Eureka Math. Geometry, Module 5. Student File_A. Contains copy-ready classwork and homework
A Story of Functions Eureka Math Geometry, Module 5 Student File_A Contains copy-ready classwork and homework Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may
Geometry CP Constructions Part I Page 1 of 4. Steps for copying a segment (TB 16): Copying a segment consists of making segments.
Geometry CP Constructions Part I Page 1 of 4 Steps for copying a segment (TB 16): Copying a segment consists of making segments. Geometry CP Constructions Part I Page 2 of 4 Steps for bisecting a segment
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
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
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
Yimin Math Centre. Year 10 Term 2 Homework. 3.1 Graphs in the number plane The minimum and maximum value of a quadratic function...
Year 10 Term 2 Homework Student Name: Grade: Date: Score: Table of contents 3 Year 10 Term 2 Week 3 Homework 1 3.1 Graphs in the number plane................................. 1 3.1.1 The parabola....................................
Exercises for Chapter Three You know you've got to exercise your brain just like your muscles. Will Rogers ( )
Exercises for Chapter Three You know you've got to exercise your brain just like your muscles. Will Rogers (1879 1935) Investigation Exercise 3.1. (a) Construct a tessellation. (Directions for construction.)
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
Math 5320, 3/28/18 Worksheet 26: Ruler and compass constructions. 1. Use your ruler and compass to construct a line perpendicular to the line below:
Math 5320, 3/28/18 Worksheet 26: Ruler and compass constructions Name: 1. Use your ruler and compass to construct a line perpendicular to the line below: 2. Suppose the following two points are spaced
Unit 1. Name. Basics of Geometry Part 1. 2 Section 1: Introduction to Geometry Points, Lines and Planes
Name Period Date Points, lines, and planes are the building blocks of geometry. What is geometry? Unit 1 Basics of Geometry Part 1 Geometry means, and it involves the properties of points, lines, planes
Section 1: Introduction to Geometry Points, Lines, and Planes
Section 1: Introduction to Geometry Points, Lines, and Planes Topic 1: Basics of Geometry - Part 1... 3 Topic 2: Basics of Geometry Part 2... 5 Topic 3: Midpoint and Distance in the Coordinate Plane Part
Concept: Solving Inequalities Name:
Concept: Solving Inequalities Name: You should have completed Equations Section 7 Part A: Solving Inequalities before beginning this handout. COMPUTER COMPONENT Instructions: In follow the Content Menu
Time To Hit The Slopes. Exploring Slopes with Similar Triangles
Time To Hit The Slopes Eploring Slopes with Similar Triangles Learning Goals In this lesson, ou will: Use an equation to complete a table of values. Graph an equation using a table of values. Use transformations
Quadratic Functions Date: Per:
Math 2 Unit 10 Worksheet 1 Name: Quadratic Functions Date: Per: [1-3] Using the equations and the graphs from section B of the NOTES, fill out the table below. Equation Min or Max? Vertex Domain Range
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
Lesson 2: Using the Number Line to Model the Addition of Integers
: Using the Number Line to Model the Addition of Integers Classwork Exercise 1: Real-World Introduction to Integer Addition Answer the questions below. a. Suppose you received $10 from your grandmother
GH Chapter 3 Quiz Review (3.1, 3.2, 3.4, 3.5)
Name: Class: Date: SHOW ALL WORK GH Chapter 3 Quiz Review (3.1, 3.2, 3.4, 3.5) Match each vocabulary term with its definition. (#1-5) a. parallel lines b. parallel planes c. perpendicular lines d. skew
Maintaining Mathematical Proficiency
Chapter 3 Maintaining Mathematical Proficiency Find the slope of the line.. y. y 3. ( 3, 3) y (, ) (, ) x x (, ) x (, ) ( 3, 3)... (, ) y (0, 0) 8 8 x x 8 8 y (, ) (, ) y (, ) (, 0) x Write an equation
Section 1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations
Section 1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations origin (x, y) Ordered pair (x-coordinate, y-coordinate) (abscissa, ordinate) x axis Rectangular or
Eureka Math. Grade 7, Module 6. Student File_A. Contains copy-ready classwork and homework
A Story of Ratios Eureka Math Grade 7, Module 6 Student File_A Contains copy-ready classwork and homework Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be
STRAIGHT LINE GRAPHS THE COORDINATES OF A POINT. The coordinates of any point are written as an ordered pair (x, y)
THE COORDINATES OF A POINT STRAIGHT LINE GRAPHS The coordinates of any point are written as an ordered pair (x, y) Point P in the diagram has coordinates (2, 3). Its horizontal distance along the x axis
Lesson 10. Homework Problem Set Sample Solutions. then Print True else Print False End if. False False True False False False
Homework Problem Set Sample Solutions 1. Perform the instructions in the following programming code as if you were a computer and your paper were the computer screen. Declare xx integer For all xx from
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
MAT 3271: Selected Solutions to the Assignment 6
Chapter 2: Major Exercises MAT 3271: Selected Solutions to the Assignment 6 1. Since a projective plan is a model of incidence geometry, Incidence Axioms 1-3 and Propositions 2.1-2.5 (which follow logically
The x coordinate tells you how far left or right from center the point is. The y coordinate tells you how far up or down from center the point is.
We will review the Cartesian plane and some familiar formulas. College algebra Graphs 1: The Rectangular Coordinate System, Graphs of Equations, Distance and Midpoint Formulas, Equations of Circles Section
Algebra Unit 2: Linear Functions Notes. Slope Notes. 4 Types of Slope. Slope from a Formula
Undefined Slope Notes Types of Slope Zero Slope Slope can be described in several ways: Steepness of a line Rate of change rate of increase or decrease Rise Run Change (difference) in y over change (difference)
Chapter 4 Graphing Linear Equations and Functions
Chapter 4 Graphing Linear Equations and Functions 4.1 Coordinates and Scatter plots on the calculator: On the graph paper below please put the following items: x and y axis, origin,quadrant numbering system,
Student Outcomes. Lesson Notes. Classwork. Example 2 (3 minutes)
Student Outcomes Students write expressions that record addition and subtraction operations with numbers. Lesson Notes This lesson requires the use of a white board for each student. Classwork Example
Rational Numbers on the Coordinate Plane. 6.NS.C.6c
Rational Numbers on the Coordinate Plane 6.NS.C.6c Copy all slides into your composition notebook. Lesson 14 Ordered Pairs Objective: I can use ordered pairs to locate points on the coordinate plane. Guiding
1.8 Coordinate Geometry. Copyright Cengage Learning. All rights reserved.
1.8 Coordinate Geometry Copyright Cengage Learning. All rights reserved. Objectives The Coordinate Plane The Distance and Midpoint Formulas Graphs of Equations in Two Variables Intercepts Circles Symmetry
Chapter 1 Section 1 Lesson: Solving Linear Equations
Introduction Linear equations are the simplest types of equations to solve. In a linear equation, all variables are to the first power only. All linear equations in one variable can be reduced to the form
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
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