4 7 Notes B
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This document provides instruction on writing and graphing linear equations in different forms. It begins with a review of equivalent forms of linear equations, including point-slope, slope-intercept, and standard form. Students are then given examples of writing equations of lines given a point and slope, or two points. The document concludes with examples of graphing lines by using the point-slope and slope-intercept forms to easily find points and draw the line. Students are challenged to graph a line given in standard form and explain their process.
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4 7 Notes A
Day 2 Opener:
- Review problem solving linear equations from the previous day
- Introduce different forms of writing linear equations: point-slope form, slope-intercept form, standard form
- Students work with a partner to practice identifying properties of lines from their equations
Section 4.7 Jiffy Graphs:
- Explain how to quickly write an equation of a line given certain information using the different forms
- Demonstrate graphing lines using point-slope and slope-intercept form by plotting points
- Ask students to consider how to graph a line in standard form for the exit slip
4.6 Notes B
This document provides instructions and examples for a skills competition involving solving equations for the variable y. Students have 5 minutes to solve 5 equations, showing their work, and circle their final answers. Correctly solving at least 4 equations earns a prize. Examples are given for finding the slope and equation of a line passing through two points, and for determining the slope from a linear equation. An exit slip assignment involves applying these skills.
Writing linear equations
1) The document provides steps for writing linear equations given the slope and a point or two points that the line passes through.
2) Examples are worked through of finding the equation of a line given its slope and one point, or given two points that the line passes through.
3) Practice problems are provided and worked through, along with a review of the process and a short quiz to assess understanding.
Complex Number's Applications
Complex numbers were first conceived by Cardano to solve cubic equations and ultimately led to the fundamental theorem of algebra. Complex numbers form an algebraically closed field where any polynomial equation has a root. Rules for addition, subtraction, and multiplication of complex numbers were developed by Bombelli. Complex numbers can be expressed as a + bi and are used throughout fields like signal processing, image processing, and more. Fractals generated from complex numbers produce beautiful patterns through iteration.
3.12 3.13 Notes A
1) The document discusses graphing equations and finding intersection points of graphs. It includes examples of graphing equations like y = x2 - 4x + 3 and finding the intersection points of the graphs y = x and y = 1000 - x.
2) Tony and Sasha's method for graphing y = x2 - 4x + 3 involved choosing x-values of 0 and -1 to plot points and draw a curve between them.
3) The document provides homework problems from pages 263 and 267 involving graphing equations and finding intersection points.
6.6 Graphing Inequalities In Two Variables
This document discusses graphing linear inequalities in two variables. It provides definitions of key terms like half-plane and boundary. It also gives helpful hints for graphing different types of inequalities based on whether the sign is >, <, ≥, or ≤ and whether it involves just x and y or a slanted line. Examples are provided to demonstrate how to graph inequalities like y > 3, x - 2, y - 3x + 2, and an applied problem involving nickels and dimes. The key steps for graphing a linear inequality on the coordinate plane are outlined.
Graphing Linear Inequalities
- A linear inequality describes a region of the coordinate plane bounded by a line. Any point in the shaded region is a solution to the inequality.
- To graph a linear inequality, first solve it for y and graph the resulting equation as a line. Then, test a point not on the line to determine which side of the line to shade based on whether it satisfies the inequality.
- The line is drawn solid for ≤ or ≥ and dashed for < or >. Shading the correct side of the line indicates the full solution set of the inequality.
3.12 3.13 Notes B
This document contains a lesson plan on graphing equations. It includes instructions for students to graph equations like y=x^2 - 4x + 3 by plotting points, determine intersection points between two graphs, and identify the region each quadrant represents on a coordinate plane. It provides guidance for students to practice graphing, identifies key ideas to remember, and assigns homework problems for students to complete.
Recommended
4 7 Notes A
Day 2 Opener:
- Review problem solving linear equations from the previous day
- Introduce different forms of writing linear equations: point-slope form, slope-intercept form, standard form
- Students work with a partner to practice identifying properties of lines from their equations
Section 4.7 Jiffy Graphs:
- Explain how to quickly write an equation of a line given certain information using the different forms
- Demonstrate graphing lines using point-slope and slope-intercept form by plotting points
- Ask students to consider how to graph a line in standard form for the exit slip
4.6 Notes B
This document provides instructions and examples for a skills competition involving solving equations for the variable y. Students have 5 minutes to solve 5 equations, showing their work, and circle their final answers. Correctly solving at least 4 equations earns a prize. Examples are given for finding the slope and equation of a line passing through two points, and for determining the slope from a linear equation. An exit slip assignment involves applying these skills.
Writing linear equations
1) The document provides steps for writing linear equations given the slope and a point or two points that the line passes through.
2) Examples are worked through of finding the equation of a line given its slope and one point, or given two points that the line passes through.
3) Practice problems are provided and worked through, along with a review of the process and a short quiz to assess understanding.
Complex Number's Applications
Complex numbers were first conceived by Cardano to solve cubic equations and ultimately led to the fundamental theorem of algebra. Complex numbers form an algebraically closed field where any polynomial equation has a root. Rules for addition, subtraction, and multiplication of complex numbers were developed by Bombelli. Complex numbers can be expressed as a + bi and are used throughout fields like signal processing, image processing, and more. Fractals generated from complex numbers produce beautiful patterns through iteration.
3.12 3.13 Notes A
1) The document discusses graphing equations and finding intersection points of graphs. It includes examples of graphing equations like y = x2 - 4x + 3 and finding the intersection points of the graphs y = x and y = 1000 - x.
2) Tony and Sasha's method for graphing y = x2 - 4x + 3 involved choosing x-values of 0 and -1 to plot points and draw a curve between them.
3) The document provides homework problems from pages 263 and 267 involving graphing equations and finding intersection points.
6.6 Graphing Inequalities In Two Variables
This document discusses graphing linear inequalities in two variables. It provides definitions of key terms like half-plane and boundary. It also gives helpful hints for graphing different types of inequalities based on whether the sign is >, <, ≥, or ≤ and whether it involves just x and y or a slanted line. Examples are provided to demonstrate how to graph inequalities like y > 3, x - 2, y - 3x + 2, and an applied problem involving nickels and dimes. The key steps for graphing a linear inequality on the coordinate plane are outlined.
Graphing Linear Inequalities
- A linear inequality describes a region of the coordinate plane bounded by a line. Any point in the shaded region is a solution to the inequality.
- To graph a linear inequality, first solve it for y and graph the resulting equation as a line. Then, test a point not on the line to determine which side of the line to shade based on whether it satisfies the inequality.
- The line is drawn solid for ≤ or ≥ and dashed for < or >. Shading the correct side of the line indicates the full solution set of the inequality.
3.12 3.13 Notes B
This document contains a lesson plan on graphing equations. It includes instructions for students to graph equations like y=x^2 - 4x + 3 by plotting points, determine intersection points between two graphs, and identify the region each quadrant represents on a coordinate plane. It provides guidance for students to practice graphing, identifies key ideas to remember, and assigns homework problems for students to complete.
Graphing inequalities in two variables
This document discusses how to graph linear inequalities in two variables. It provides examples of graphing different types of inequalities, such as x < 2, y ≥ 3, and x + y < 3. The key steps are to first graph the corresponding equal sign equation, and then determine which side of the line to shade based on whether the inequality sign is <, >, ≤, or ≥. Shading goes to the left or below the line for < or ≤, and to the right or above the line for > or ≥.
11.6 graphing linear inequalities in two variables
This document discusses how to graph linear inequalities in two variables. It provides examples of graphing various inequalities, including 2x + 3y ≤ 6, 2x + y > 3, and y < 3x. The process involves graphing the boundary line defined by the equal case of the inequality and then shading the appropriate region based on checking if a test point satisfies the inequality. Key steps are to draw the boundary line as solid or dashed based on the symbols (< or > versus ≤ or ≥) and then shade the region containing points that satisfy the inequality.
Functions lesson
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- Representing functions in tables, graphs, and equations
- Identifying linear, quadratic, and exponential functions
- Adding, subtracting, and inverting functions
It provides examples and interactive exercises to help explain these fundamental function concepts.
Math Functions
This document provides an overview of different types of functions that may be assessed on the ACT exam, including linear, quadratic, trigonometric, logarithmic, and exponential functions. It discusses key concepts for each type of function such as domain and range, asymptotes, amplitude and period for trig functions, and properties of logarithmic and exponential growth/decay functions. Examples are provided to illustrate how to work with each function type, including solving equations, finding features of graphs, and recognizing standard forms.
Math Number Quantity
The document provides an overview of topics related to numbers and quantities that may appear on the ACT exam, including:
I. Real and complex number systems, rational vs irrational numbers, integers, whole numbers, natural numbers. Converting between fractions, mixed numbers, and improper fractions. Comparing fractions. (Paragraphs 1-13)
II. Counting consecutive integers, using the number line to locate numbers and find distances. Radicals, simplifying square roots. (Paragraphs 14-23)
III. The complex number system, imaginary numbers, and the complex plane. Greatest common factors and least common multiples, using calculators to find them. (Paragraphs 24-25)
Math Geometry
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The document is a math worksheet from Xinmin Secondary School for students in class 3E on graphing exponential and logarithmic functions. It contains 6 questions asking students to sketch various exponential and logarithmic graphs and identify intercepts, asymptotes and solutions to related equations by finding the intersection points of the graphs. Students are reminded to clearly label their graphs and ensure they are large enough.
coordinate_geometry
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Straight line graphs
This document is a resource pack for a GCSE Mathematics unit on quadratic equations. It contains 9 questions about straight line graphs and their equations. The questions cover identifying gradients and y-intercepts, plotting points and lines, writing equations of lines parallel to given lines, and representing inequalities graphically. Students are asked to find gradients, intercepts, coordinates of intersection points, and match lines to their equations.
Magic square made easy
Magic Square in 3 easy steps:
1. Form a square matrix with numbers 1 to n^2 in sequence, where n is the order of the magic square.
2. Form two matrices of the same size, one for identifying rows and one for columns, with middle columns numbered 1 to n and columns on either side getting smaller or larger by 1.
3. Superimpose the row and column matrices to find the number in each cell of the final magic square matrix from the corresponding entries in the first matrix.
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This document discusses how to graph linear equations in slope-intercept form. It defines key terms like slope, y-intercept, rise over run, and slope-intercept form. It explains that the slope is the rate of change between x and y and the y-intercept is the point where the line crosses the y-axis. The document provides examples of graphing different types of lines and reviews the steps to graph any equation in slope-intercept form.
Multiplication of two 3 d sparse matrices using 1d arrays and linked lists
A basic algorithm of 3D sparse matrix multiplication (BASMM) is presented using one dimensional (1D) arrays which is used further for multiplying two 3D sparse matrices using Linked Lists. In this algorithm, a general concept is derived in which we enter non- zeros elements in 1st and 2nd sparse matrices (3D) but store that values in 1D arrays and linked lists so that zeros could be removed or ignored to store in memory. The positions of that non-zero value are also stored in memory like row and column position. In this way space complexity is decreased. There are two ways to store the sparse matrix in memory. First is row major order and another is column major order. But, in this algorithm, row major order is used. Now multiplying those two matrices with the help of BASMM algorithm, time complexity also decreased. For the implementation of this, simple c programming and concepts of data structures are used which are very easy to understand for everyone.
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This document provides instruction on writing and graphing linear equations in slope-intercept and standard form. It includes examples of finding the slope and y-intercept from an equation in slope-intercept form, writing an equation given the slope and y-intercept, graphing lines from their equations, finding x- and y-intercepts to graph in standard form, and transforming between the two forms. Students are provided practice problems to complete for homework.
Alg2.5 A Notes
1. The document provides examples to evaluate the expression 2(x+1) for different values of x, and asks students to explain why 2(x+1) is always even and 2(x)+1 is always odd when x is an integer.
2. Students are given a homework assignment involving basic algebraic rules and properties. They complete an activity with a partner involving these rules.
3. The document asks students to rephrase basic algebraic rules without using variables, evaluate expressions using properties like distributive property, and find products of fractions. Patterns in the products are explored.
4. Homework assigned includes a mini quiz, practice problems, and studying for an upcoming test.
2.5 notes b
This document contains notes and instructions for a math lesson that includes:
1) Solving expressions and evaluating them for given values.
2) Completing an in-class activity with partners to review basic arithmetic rules.
3) Practicing the basic rules of arithmetic through examples of simplifying expressions using properties like commutative, associative, and distributive properties.
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Chapter 2 problems
This document provides examples and solutions for accounting problems involving the calculation of earnings per share, gross profit margin, operating profit, and the proper ordering and formatting of income statement items and full income statements. It includes sample income statements for Frantic Fast Foods, Bettis Bus Company, Hillary Swank Clothiers, A-Rod Fishing Supplies, Dental Drilling Company, and Jonas Brothers Cough Drops using financial information provided.
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- Domain and range
- Representing functions in tables, graphs, and equations
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- Adding, subtracting, and inverting functions
It provides examples and interactive exercises to help explain these fundamental function concepts.
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This document provides an overview of different types of functions that may be assessed on the ACT exam, including linear, quadratic, trigonometric, logarithmic, and exponential functions. It discusses key concepts for each type of function such as domain and range, asymptotes, amplitude and period for trig functions, and properties of logarithmic and exponential growth/decay functions. Examples are provided to illustrate how to work with each function type, including solving equations, finding features of graphs, and recognizing standard forms.
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II. Counting consecutive integers, using the number line to locate numbers and find distances. Radicals, simplifying square roots. (Paragraphs 14-23)
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Exp&log graphs assignment
The document is a math worksheet from Xinmin Secondary School for students in class 3E on graphing exponential and logarithmic functions. It contains 6 questions asking students to sketch various exponential and logarithmic graphs and identify intercepts, asymptotes and solutions to related equations by finding the intersection points of the graphs. Students are reminded to clearly label their graphs and ensure they are large enough.
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2. Form two matrices of the same size, one for identifying rows and one for columns, with middle columns numbered 1 to n and columns on either side getting smaller or larger by 1.
3. Superimpose the row and column matrices to find the number in each cell of the final magic square matrix from the corresponding entries in the first matrix.
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Alg2.5 A Notes
1. The document provides examples to evaluate the expression 2(x+1) for different values of x, and asks students to explain why 2(x+1) is always even and 2(x)+1 is always odd when x is an integer.
2. Students are given a homework assignment involving basic algebraic rules and properties. They complete an activity with a partner involving these rules.
3. The document asks students to rephrase basic algebraic rules without using variables, evaluate expressions using properties like distributive property, and find products of fractions. Patterns in the products are explored.
4. Homework assigned includes a mini quiz, practice problems, and studying for an upcoming test.
2.5 notes b
This document contains notes and instructions for a math lesson that includes:
1) Solving expressions and evaluating them for given values.
2) Completing an in-class activity with partners to review basic arithmetic rules.
3) Practicing the basic rules of arithmetic through examples of simplifying expressions using properties like commutative, associative, and distributive properties.
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Chapter 2 problems
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Chapter 2 basic financial statements exercise
Here are the adjustments to the balance sheet after the loss of the barn and shed:
Assets:
Barns and Sheds - $23,800
Owner's Equity:
Hollis Roberts, capital - $23,800
All other line items remain the same. The accounting equation is still balanced after adjusting for the loss.
Problem 2.7
Preparing an Income Statement
The following information is for J.C. Landscaping for the month of May:
Revenues from landscape design and installation services: $42,500
Cost of goods sold (direct materials and labor): $21,750
Salaries expense: $9,000
Rent
Chapter 2 answers
- The document appears to be a journal for a company with various transactions in August 2014, including the purchase of office supplies, payment of rent, collection of fees, and payment of expenses like advertising and salaries.
- The general ledger accounts show debits and credits for cash, accounts receivable, prepaid insurance, accounts payable, and other expense and revenue accounts.
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Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
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3-7
Objective To graph and write linear equations
Ski resorts often use steepness to rate the difficulty
of their hills. The steeper the hill, the higher the
difficulty rating. Below are sketches of three new hills
at a particular resort. Use each rating level only once.
Which hill gets which rating? Explain.
Difficulty Ratings
Easiest
Intermediate
Difficult
3300 ft 3000 ft 3500 ft
1190 ft 1180 ft 1150 ft
A B C
Th e Solve It involves using vertical and horizontal distances to determine steepness.
Th e steepest hill has the greatest slope. In this lesson you will explore the concept of
slope and how it relates to both the graph and the equation of a line.
Essential Understanding You can graph a line and write its equation when you
know certain facts about the line, such as its slope and a point on the line.
Equations of Lines in the
Coordinate Plane
Think back!
What did you
learn in algebra
that relates to
steepness?
Key Concept Slope
Defi nition
Th e slope m of a line is the
ratio of the vertical change
(rise) to the horizontal change
(run) between any two points.
Symbols
A line contains the
points (x1, y1) and
(x2, y2) .
m 5
rise
run 5
y2 2 y1
x2 2 x1
Diagram
(x2, y2)
(x1, y1)
O
x
y run
rise
Lesson
Vocabulary
• slope
• slope-intercept
form
• point-slope form
L
V
L
V
• s
LL
VVV
• s
hsm11gmse_NA_0307.indd 189 2/24/09 6:49:09 AM
http://media.pearsoncmg.com/aw/aw_mml_shared_1/copyright.html
Problem 1
Got It?
190 Chapter 3 Parallel and Perpendicular Lines
Finding Slopes of Lines
A What is the slope of line b?
m 5
2 2 (22)
21 2 4
5 4
25
5 245
B What is the slope of line d?
m 5
0 2 (22)
4 2 4
5 20 Undefi ned
1. Use the graph in Problem 1.
a. What is the slope of line a?
b. What is the slope of line c?
As you saw in Problem 1 and Got It 1 the slope of a line can be positive, negative,
zero, or undefi ned. Th e sign of the slope tells you whether the line rises or falls
to the right. A slope of zero tells you that the line is horizontal. An undefi ned slope
tells you that the line is vertical.
You can graph a line when you know its equation. Th e equation of a line has diff erent
forms. Two forms are shown below. Recall that the y-intercept of a line is the
y-coordinate of the point where the line crosses the y-axis.
O
y
c
b
d a
x
2
2 86
4
6
( 1, 2)
(4, 2)
(4, 0)
(5, 7)(1, 7)
(2, 3)
Positive slope
O
x
y
Negative slope
O
x
y
Zero slope
O
x
y
Undefined slope
O
x
y
Key Concept Forms of Linear Equations
Defi nition
Th e slope-intercept form of an equation of
a nonvertical line is y 5 mx 1 b, where m
is the slope and b is the y-intercept.
Symbols
Th e point-slope form of an equation of a
nonvertical line is y 2 y1 5 m(x 2 x1),
where m is the slope and (x1, y1) is a point
on the line.
y mx b
slope y-intercept
y y1 m(x x1)
slope x-coordinatey-coordinate
A
...
January 21, 2015
1. The document provides information on linear functions and how to determine if an equation represents a linear function. It discusses using standard form (Ax + By = C) to identify linear equations and determine intercepts.
2. The document contains examples of writing equations of lines given points and slopes in various forms. It discusses using point-slope form and converting between slope-intercept and standard form.
3. The document provides practice problems determining if graphs are functions, whether equations represent lines, finding rates of change, intercepts, and writing equations in different forms. It aims to help students work with linear functions and equations.
Notes Day 6
1. The document provides instructions and examples for solving problems involving midpoint and distance formulas, as well as transformations in the coordinate plane. Practice problems are given for finding midpoints and distances between points, as well as homework instructions.
2. Key terms related to transformations are defined, including reflection, rotation, translation, arrow notation, and the rule for describing translations.
3. Examples are given of transformations, including reflections across lines and rotations about points. Formulas and notation for describing translations are also provided.
local_media5416891530663583326.ppt
This document provides instruction on calculating and understanding slope. It defines slope as the steepness of a line and discusses how to calculate slope given two points on a line using the rise over run formula or the slope formula. It provides examples of finding the slope of lines from their graphs or given two points and discusses the slopes of horizontal and vertical lines.
FindingSlope.ppt
This document provides instruction on calculating and understanding slope. It defines slope as the steepness of a line and discusses how to calculate slope given two points on a line using the rise over run formula or the slope formula. It provides examples of finding the slope of lines from their graphs or given two points and discusses the slopes of horizontal and vertical lines.
3.3 Notes B
This document provides instruction and examples for calculating distance and absolute value. It begins by asking the reader to calculate the distance between several pairs of points on a coordinate plane. It then defines absolute value as the distance between two numbers and provides examples of calculating absolute values. The document continues with more practice problems calculating absolute values and rewriting expressions using absolute value notation. It concludes by explaining how to solve equations involving absolute values and providing an example of using the Pythagorean theorem to calculate the distance between two points.
3.3 Notes B
This document provides instruction and examples for calculating distance and absolute value. It begins by asking the reader to calculate the distance between several pairs of points on a coordinate plane. It then defines absolute value as the distance between two numbers and provides examples of calculating absolute values. The document continues with more practice problems calculating absolute values and rewriting expressions using absolute value notation. It concludes by explaining how to solve equations involving absolute values and providing an example of using the Pythagorean theorem to calculate the distance between two points.
Math Algebra
The document provides an overview of key algebra concepts covered on the ACT exam, including expressions, equations, inequalities, functions, and quadratic equations. It discusses how to simplify and combine like terms in expressions, solve different types of equations (linear, quadratic, absolute value), factor expressions using techniques like greatest common factor and difference of squares, work with fractions and systems of equations. Example problems and step-by-step explanations are provided for many of the concepts. The document is intended as a review of essential algebra skills and strategies for tackling related questions that may appear on the ACT.
4 10 Notes B
This document contains homework questions and examples about solving systems of equations using substitution. It includes:
1) A race between Demitri and Yakov with distance-time graphs and questions about their speeds and when Yakov overtakes Demitri.
2) Three examples walking through the substitution method to solve systems of equations step-by-step. The examples find the intersection point of lines and solve systems algebraically.
3) Questions checking understanding of what it means for something to be a solution to a system of equations and what the solution represents.
Linear Functions Presentation
My final project that was to be a PowerPoint that could be worked on by individual students. This PowerPoint goes over linear functions.
April 13, 2015
This document contains information about a math class that is reviewing quadratic functions. It includes:
1. An outline of the class agenda which focuses on reviewing key concepts like how the b-value affects the parabola and completing classwork.
2. Details about grading which includes assignments, homework, tests, the final exam, and notebook checks.
3. Sample problems and class notes focused on quadratic functions, including the axis of symmetry, vertex, graphing techniques, and how changing a, b, and c values impacts the parabola.
4. Examples of completing the steps to graph quadratic functions like plotting points and reflecting over the axis of symmetry.
Alg II 2-3 and 2-4 Linear Functions
This document provides an overview of key concepts in Algebra II Chapter 2 on functions, equations, and graphs. It introduces the concept of slope as the ratio of vertical to horizontal change between points on a line. Students will learn to graph linear equations, write equations of lines given slope and a point, and identify parallel and perpendicular lines based on their slopes. The objectives are to graph and write equations of lines in different forms including slope-intercept, point-slope, and standard form.
Finding slope
The document discusses slope and how to calculate it given points on a line or its graph. It provides examples of finding the slope between two points using the rise over run formula or slope formula. It explains that horizontal lines have a slope of 0 and vertical lines have undefined slope. It also gives an example of solving for an unknown value in one of the points when given the other point and slope.
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Unit 1 test 2.9 notes b
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
2.2 2.3 notes a
The document describes a numeric pattern where each row contains consecutive odd integers centered around 1. It asks students to conjecture the pattern and sum of terms in each row. It also provides homework questions on conditional statements, deductive reasoning, and analyzing the truth value of related conditional statements.
Unit 1 test 2.9 notes a
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
2.8 notes a
1. The document discusses solving equations by backtracking. It begins by defining an equation and identifying true and false equations. It then discusses the concept of solutions - the values that make the equation true.
2. Examples are provided to illustrate finding solutions to equations by reversing the steps of number tricks. Backtracking involves working backwards through the operations to determine the starting value.
3. Readers are instructed to solve sample equations by listing the number trick steps and then reversing the steps through backtracking to find the solution values.
Chapter 1 rev notes (a)
This document provides homework questions and a review packet for a chapter. It lists 7 numbered sections that appear to be questions or tasks related to reviewing material from the first chapter. The document aims to help students review and reinforce their understanding of the concepts covered in the initial chapter through completing the homework and review activities.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations (translations, reflections, rotations, and dilations) and provides examples of identifying each type using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations - translations, reflections, rotations, and dilations - and provides examples of identifying each type of transformation using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. It includes examples of using the midpoint formula to find the midpoint of a segment and using given midpoints and endpoints to find missing endpoints.
3. There are also examples of using the Pythagorean theorem and distance formula to find the length of a segment between two points.
1.5 1.6 notes a
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6. Students are asked to work on vocabulary and postulates after the quiz.
2. Examples are given for finding midpoints and distances between points on a coordinate plane using formulas like the midpoint formula, Pythagorean theorem, and distance formula.
3. Homework assignments include problems from the textbook on the topics of formulas in geometry, midpoints, and distance.
2.6 2.7 notes a
1. The document provides instructions and tasks for students to complete mathematical expressions, homework questions, and a lesson on reversible and non-reversible operations.
2. Students are asked to simplify expressions, complete homework problems, and determine whether example operations are reversible by considering if the starting number can be determined.
3. The document demonstrates how to "backtrack" through a multi-step operation to find the original starting number using reversible operations.
2.4 notes b
1. Students were asked to put math problems on the board from previous homework. The document then provides examples of expressions and teaches how to simplify them using order of operations and properties like the distributive property. Students are asked to simplify sample expressions involving variables.
2. The document reviews that expressions need to have "like terms" to be simplified, such as terms with the same variables. Students practice simplifying expressions with multiple variables and terms by combining like terms.
3. To conclude, students are instructed to write their name and ID number on raffle tickets and provide just the simplified answer, practicing the skills of defining a variable, writing an expression, simplifying it, and evaluating it.
2.3 notes b
This document contains instructions for students to complete various math exercises on their TI-Nspire calculators. It asks students to match expressions to steps, write an expression for the area of a rectangle, simplify an algebraic expression, evaluate expressions for different variable values, and complete an activity on their calculators worth daily work points. Students are told to work with partners but can ask other group members for help if needed and to raise their hand once finished.
2.2 notes a
1. When entering class each day, students should say hi, have their homework out, write any questions on the board, and start the opener problem.
2. The document then provides examples of algebra problems involving variables to represent unknown quantities and expressions combining variables, operators, and constants.
3. Students are instructed to complete a set of practice problems from page 94 in their workbook and have their work checked by the teacher.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions on graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages. Finally, it addresses solving an equation like x^3 + 5x = 7x^2 - 5 by graphing and reflects on graphing techniques from prior lessons.
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4 7 Notes B
- 1. Day 2: Opener Think back: Complete the following problem on a math raffle ticket. Good Luck! 1. Write the equation of the line that is parallel to x = ‐6 and passes through the point (3,10). 1
- 2. Homework Questions: 2
- 3. 3
- 4. 4
- 5. Section 4.7 Jiffy Graphs TOPIC ONE (cont.) Solve your given equation for y. Information from Equations Think back: Are these equations equivalent? How do you know? Since they are equivalent then they should all be the same line! This means they should all have the same __________, ________________, and ___________. It's Your Turn! Complete the following 1. What is the slope of line l ? 4 questions with your partner.(5 minutes) 2. Where does l cross the y‐axis? 3. Where does l cross the x‐axis? 4. Which equation for l makes it easiest to see that the point (5,3) is on the line? Explain. 5
- 6. Linear Equation Forms Point‐Slope Form (IYT # 1 & 4): • • Slope‐Intercept Form (IYT # 1 & 2): • • Standard Form (IYT # 3): • • 6
- 7. TOPIC TWO We can use the different forms of linear equations that we Writing equations of learned today to write the equation of a line in a jiffy! lines using the different forms. Given slope and through (10, ‐3) with slope 7 the given point: (Ex. #1) Step 1: Substitute the given information into point‐slope form. Step 2: Simplify to slope‐intercept form (solve for y). Given 2 points: (Ex. # 2) (0,7) and (‐4,9) Step 1: Find the slope between these 2 points. Step 2: Substitute one of the points and the slope into point‐ slope form. Step 3: Simplify to slope‐intercept form (solve for y). 7
- 8. TOPIC THREE Think back: How did we graph equations last chapter? Jiffy Graphing We are going to use the forms of linear equations to help us graph in a jiffy! Using Point‐Slope Graph y+2 = ‐3(x+1). Form: (Ex. # 3) Step 1: Plot the given point. Step 2: Use the slope to plot two more points. Step 3: Connect all three points with a line. Using Slope‐Intercept Graph y = 1.75x ‐1. Form: (Ex.#4) Step 1: Plot your y‐intercept. Step 2: Use the slope to plot two more points. Step 3: Connect all three points with a line. 8
- 9. Exit Slip: 1.) Think about how you might graph the equation of a line given to you in standard form. Write down what your method would be on a half‐sheet of paper and turn it in before you leave. Think back: What information can you easily get from standard form? OR Can you change it to an equivalent form? 2.) Graph 3x+4y = 12 using your method. 9
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