Linear Inequalities
3 likes821 views
This document discusses how to graph linear inequalities on a coordinate plane. It explains that less than and greater than signs are represented by dashed lines, while less than or equal to and greater than or equal to signs use solid lines. It notes that inequalities must be written in slope-intercept form before graphing and that the shading depends on whether the inequality involves less than or greater than. Specifically, y greater than inequalities are shaded above the line and y less than inequalities are shaded below the line. Practice graphing many problems to fully understand how to determine the shading direction.
1 of 12
Recommended
Linear Inequalities
Linear InequalitiesBitsy Griffin
Ìý
This document discusses how to graph linear inequalities on the number line and coordinate plane. It explains that less than and greater than signs are represented by dashed lines, while less than or equal to and greater than or equal to signs use solid lines. When graphing linear inequalities with both x and y, the equation must be in slope-intercept form. A dashed line is used if the sign is less than or greater than, and shading is done above or below the line depending on whether the inequality is greater than or less than.Limits!
Limits!glenns
Ìý
This document defines and explains key limits concepts in mathematics including intended height, approaching a limit from the right or left, holes, asymptotes, vertical asymptotes, horizontal asymptotes, and slant asymptotes. It states that the sign after the number being approached indicates the side of the graph and discusses factors that do and do not cancel in determining asymptotes or holes.Stretching & Shrinking 2.2 Summary + Tests For Similarity
Stretching & Shrinking 2.2 Summary + Tests For SimilarityKathy Favazza
Ìý
The document discusses coordinate transformations on shapes. It notes that adding or subtracting from the x-coordinate moves a shape left or right, and adding or subtracting from the y-coordinate moves a shape up or down. Multiplying both coordinates by the same number shrinks the shape, keeping it similar, while multiplying by different numbers makes the shape not similar to the original.Day 5 examples u3f13
Day 5 examples u3f13jchartiersjsd
Ìý
Polynomial functions are algebraic expressions with variables raised to whole number powers. They can be classified based on their degree as linear, quadratic, cubic, quartic, or quintic. The graph of a polynomial is smooth and continuous without sharp corners. Polynomials can also be described based on having an odd or even degree, which determines their end behavior as the variable approaches positive or negative infinity. The key characteristics used to identify a polynomial function include its degree, leading coefficient, even/odd classification, number of x-intercepts, and number of local maxima and minima points.Completing the square
Completing the squareStreet Bears
Ìý
The document discusses completing the square and solving quadratic equations. It explains that completing the square allows any quadratic equation to be written in the form (x - h)2 = k, which can then be solved using the square root property. The quadratic formula is derived from completing the square and provides a general method for solving any quadratic equation in one variable by setting it equal to 0 and substituting the coefficients into the formula. Examples are provided to demonstrate how to use completing the square and the quadratic formula to solve quadratic equations.4 Figure Grid References
4 Figure Grid Referencesigrant
Ìý
The document explains how to use a four figure grid reference system to locate positions on a map. A four figure grid reference specifies the square kilometer grid square in the bottom left corner by providing the line numbers of the two pairs of figures. Several examples are given of identifying the grid square that contains different landmarks on sample maps.[Final] Math Ch 4 7 Lesson![[Final] Math Ch 4 7 Lesson](https://cdn.slidesharecdn.com/ss_thumbnails/finalmath-ch4-7lesson-100326012847-phpapp02-thumbnail.jpg?width=560&fit=bounds)
[Final] Math Ch 4 7 Lessoncolleenyee
Ìý
The document discusses solving radical inequalities and provides steps to graph the domain of a radical inequality:
1. Set all radicals equal to zero and solve for the variable to obtain critical numbers.
2. Ignore the inequality and solve as an equation to find more critical numbers.
3. Draw a number line with intervals at the critical numbers and test values in the original inequality, shading intervals where it is true and crossing out where false.
4. Shade the domain of the inequality on the number line based on the values possible for the variable.
An example problem walks through these steps to graph the domain of an inequality. Practice problems are provided to reinforce the process.Graphing polynomials
Graphing polynomialsmakenziew1
Ìý
The document discusses how to graph polynomials by determining the x-intercepts from the zeros of the polynomial, the y-intercept, and the behavior at infinity using the leading coefficient test. It provides details on how the multiplicity of zeros relates to whether x-intercepts cross or touch the x-axis, and whether the graph is flat at those points. An example graphing the polynomial f(x)=x^5-5x^4+10x^3-10x^2+5x-40 is worked through step-by-step.Integers
Integersgrade5a
Ìý
Integers are positive numbers, negative numbers, or zero, but not fractions or decimals. Positive integers are whole numbers greater than zero to the right of zero on the number line, while negative integers are whole numbers less than zero to the left of zero. Negative numbers are represented by a minus sign and result from a subtraction where the number being taken away is larger. Positive numbers are greater than zero and represented by a plus sign. The number line helps show addition and subtraction of integers.Fractions on a number line
Fractions on a number linenikkilouiseuk
Ìý
This document discusses placing fractions on a number line. It explains that a fraction represents a piece of a whole, where the whole is equal to 1. The fraction belongs between 0 and 1 on the number line. It provides examples of drawing number lines divided into halves, thirds, fifths, and other fractions, where the number line is separated into equal pieces based on the fractional parts being represented. Activities are suggested to draw number lines for various fractions such as thirds, quarters, sixths, tenths and twelfths.Bingo
BingoAshtinFlener
Ìý
This document discusses polynomial functions, including their end behavior depending on whether the degree is even or odd. It also covers factored form, standard form, and how to solve polynomials using box and diamond steps or synthetic division. The key steps for synthetic division are listed as writing down coefficients in order, drawing a box and line while switching signs of the number dividing, dropping the first number down, and repeating multiplication.Lattice Mult. V2
Lattice Mult. V2LilianPatrick
Ìý
Lattice multiplication is a method for multiplying multi-digit numbers by drawing a grid and placing the numbers to be multiplied along the sides. For each box in the grid, the number above is multiplied by the number to the right and the products are written in the boxes. The numbers are then added along the diagonals, with carries as needed, and the final sum is the answer. The document provides examples of multiplying a 2-digit by 1-digit number and a 2-digit by 2-digit number using the lattice method.Double bottom reversal pattern
Double bottom reversal patternMike Auten
Ìý
The double bottom reversal pattern describes a setup where a stock hits a low twice within a downtrend, each followed by an increase of over 10%, before breaking through a resistance level and confirming it as new support. This signals the potential reversal of the downtrend, allowing traders to initiate a long position with the previous resistance level as the profit target. For a true double bottom, six specific criteria must be met including two bottoms, two increases, a resistance breakdown, and resistance turning to support.Mathematics of investigation
Mathematics of investigationNonie Diaz
Ìý
This document describes a study that aims to find a formula to calculate the total number of trapezoids in an N-layered triangle. It first explains how to construct an N-layered triangle by adding triangles to an existing triangle to form additional layers. It then presents tables and figures that count the number of upright and inverted trapezoids in each layer of sample N-layered triangles. Using this data, it derives finite difference formulas to calculate the number of upright and inverted trapezoids as functions of N. It combines these formulas to arrive at the final formula: TNT = n(n3 + 35n/4 - n2 - 29) + 33, which calculates the total number of7.5 Systems Of Inequalities
7.5 Systems Of Inequalitiesramjdram
Ìý
This document provides instructions for graphing linear inequalities on a coordinate plane. It explains that linear inequalities are graphed as lines but must be shaded according to the inequality sign. To graph an inequality, one must first put it in slope-intercept form, then graph the line as dashed or solid based on the inequality sign, and lastly shade the appropriate region indicated by the inequality sign.System of linear inequalities
System of linear inequalitiesmstf mstf
Ìý
Here is the system of inequalities for the cross-country team problem:
Let x = number of water bottles sold to students
Let y = number of water bottles sold to others
x + y ≤ 100 (they have 100 bottles total)
3x + 5y ≥ 400 (they need at least $400)
Graph the regions defined by these inequalities and the overlapping region is the solution.Linear Equations
Linear Equationsrfant
Ìý
Students learn to define and identify linear equations. They also learn the definition of Standard Form of a linear equation.
Students also learn to graph linear equations using x and y intercepts.Linear equations
Linear equationshireshgupta1997
Ìý
This document discusses linear equations in one variable. It defines linear equations as those involving single variables with the highest power being 1. It presents rules for solving linear equations, including adding, subtracting, multiplying, or dividing the same quantity to both sides. Transposition as a method is explained, where terms change signs when shifted between sides of an equation. Examples of solving linear equations are provided. The document also discusses applying linear equations to word problems by setting up the equation based on the problem and solving for the unknown variable. Several examples of solving word problems involving linear equations are presented.Linear Equation with One Variable (LEOV)
Linear Equation with One Variable (LEOV)SMPK Penabur Gading Serpong
Ìý
1) The document discusses linear equations with one variable (LEOV). It defines key terms like statements, open and closed sentences, equations, and the components of a linear equation with one variable.
2) Examples are provided to illustrate open sentences that can be made into closed sentences or equations by replacing variables with values. Exercises ask the reader to write open sentences as equations and solve simple equations.
3) The final section directs the reader to solve two sample linear equations with one variable, tying together the concepts discussed in the document. Linear Equation In one variable class 7
Linear Equation In one variable class 7Poulami Choudhury
Ìý
This document defines and provides examples of linear equations in one variable. It explains that a linear equation is an equation that can be written in the form ax + b = c or ax = b, where a, b, c are constants and a ≠0. Examples of linear equations given include 3x + 9 = 0 and 7x + 5 = 2x - 9. The document also discusses how to determine if a value is a solution to a linear equation by substitution and simplification. Steps for solving linear equations are provided, which include isolating the variable using inverse operations like addition/subtraction and multiplication/division.linear equation
linear equationkanishkaanandkv
Ìý
1) The document discusses linear equations in two variables, including defining their form as ax + by = c, explaining that they have infinitely many solutions, and noting that their graphs are straight lines.
2) Specific topics covered include finding solutions, drawing graphs, identifying equations for lines parallel to the x-axis and y-axis, and providing examples of writing and solving linear equations.
3) The summary restates the key points about the properties of linear equations in two variables, such as their graphical and algebraic representations.Chapter 3. linear equation and linear equalities in one variables
Chapter 3. linear equation and linear equalities in one variablesmonomath
Ìý
Here are the steps to solve this inequality problem:
1) Write an expression for the perimeter in terms of x
2) Set the perimeter expression ≤ 40
3) Isolate x by undoing the operations
4) Write the solution set
The solution is 0 ≤ x ≤ 7Solution of linear equation & inequality
Solution of linear equation & inequalityDalubhasaan ng Lungsod ng Lucena
Ìý
The document discusses solving linear equalities and inequalities with one variable. It defines key terms like equations, inequalities, and linear equations. It then provides steps for solving different types of linear equations and inequalities by collecting like terms, adding/subtracting the variable term to one side, and multiplying/dividing both sides by constants. The document also explains how to graph solutions to inequalities on a number line, indicating open and closed circles based on the inequality symbols. Examples are provided of solving and graphing various linear equalities and inequalities with one variable.Linear Equations and Inequalities in One Variable
Linear Equations and Inequalities in One Variablemisey_margarette
Ìý
The document discusses linear equations and inequalities in one variable. It defines linear equations and inequalities, and describes methods for solving them including: guess-and-check, cover-up, and working backwards. It also covers properties of equality and inequality, and provides examples of solving linear equations and inequalities using these properties and graphical representations of solution sets on number lines.Linear Inequality slayerix
Linear Inequality slayerixAshams kurian
Ìý
1) Solving linear inequalities involves using the same concepts as solving linear equations to isolate the variable, but inequalities have infinite solutions rather than a single solution.
2) Inequality signs (<, >, ≤, ≥) indicate whether values are less than, greater than, less than or equal to, or greater than or equal to another value.
3) Graphing linear inequalities on a number line or coordinate plane involves graphing the corresponding equality and then shading the appropriate side based on the inequality sign and whether it includes the endpoint or not.
Graphing inequalities in two variables
Graphing inequalities in two variablesJessica Garcia
Ìý
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 ≥.Math Benchmark Part 1
Math Benchmark Part 1Innos
Ìý
An asymptote is a line that a graph approaches but never touches. There are two types of asymptotes: horizontal asymptotes, which are horizontal lines a graph approaches, and vertical asymptotes, which are vertical lines a graph approaches. As a graph gets closer to an asymptote, the space between the graph and asymptote decreases infinitely. Vertical asymptotes occur when factors in the denominator equal zero and do not cancel out factors in the numerator.Graphing sytems inequalities
Graphing sytems inequalitiesJessica Garcia
Ìý
This document provides instructions for graphing systems of linear inequalities:
- Graph each inequality individually by plotting points, drawing the line, and shading the correct region based on whether it is <, ≤, >, or ≥
- Find the overlapping region that satisfies both inequalities, which is the solution to the full system
- An example graphs two inequalities and finds the overlapping purple region as the solution
- Vertices can be found by setting the equations of intersecting lines equal to each otherGraphing inequalities
Graphing inequalitiesmooca76
Ìý
This document discusses how to graph inequalities involving vertical and horizontal lines. It explains that an equation like x=2 graphs as a vertical line where all x values are equal to 2. Inequalities like x≥2 graph the line first and then shade the area indicated by the inequality. Similarly, an equation like y=0 graphs as a horizontal line, and inequalities like y≤0 graph the line and shade the appropriate area. The document also notes that ≤ and ≥ use a solid line when graphing, while > and < use a dotted line. It provides an example of writing a system of inequalities for a solution involving different bounds for x and y values.More Related Content
What's hot (6)
Integers
Integersgrade5a
Ìý
Integers are positive numbers, negative numbers, or zero, but not fractions or decimals. Positive integers are whole numbers greater than zero to the right of zero on the number line, while negative integers are whole numbers less than zero to the left of zero. Negative numbers are represented by a minus sign and result from a subtraction where the number being taken away is larger. Positive numbers are greater than zero and represented by a plus sign. The number line helps show addition and subtraction of integers.Fractions on a number line
Fractions on a number linenikkilouiseuk
Ìý
This document discusses placing fractions on a number line. It explains that a fraction represents a piece of a whole, where the whole is equal to 1. The fraction belongs between 0 and 1 on the number line. It provides examples of drawing number lines divided into halves, thirds, fifths, and other fractions, where the number line is separated into equal pieces based on the fractional parts being represented. Activities are suggested to draw number lines for various fractions such as thirds, quarters, sixths, tenths and twelfths.Bingo
BingoAshtinFlener
Ìý
This document discusses polynomial functions, including their end behavior depending on whether the degree is even or odd. It also covers factored form, standard form, and how to solve polynomials using box and diamond steps or synthetic division. The key steps for synthetic division are listed as writing down coefficients in order, drawing a box and line while switching signs of the number dividing, dropping the first number down, and repeating multiplication.Lattice Mult. V2
Lattice Mult. V2LilianPatrick
Ìý
Lattice multiplication is a method for multiplying multi-digit numbers by drawing a grid and placing the numbers to be multiplied along the sides. For each box in the grid, the number above is multiplied by the number to the right and the products are written in the boxes. The numbers are then added along the diagonals, with carries as needed, and the final sum is the answer. The document provides examples of multiplying a 2-digit by 1-digit number and a 2-digit by 2-digit number using the lattice method.Double bottom reversal pattern
Double bottom reversal patternMike Auten
Ìý
The double bottom reversal pattern describes a setup where a stock hits a low twice within a downtrend, each followed by an increase of over 10%, before breaking through a resistance level and confirming it as new support. This signals the potential reversal of the downtrend, allowing traders to initiate a long position with the previous resistance level as the profit target. For a true double bottom, six specific criteria must be met including two bottoms, two increases, a resistance breakdown, and resistance turning to support.Mathematics of investigation
Mathematics of investigationNonie Diaz
Ìý
This document describes a study that aims to find a formula to calculate the total number of trapezoids in an N-layered triangle. It first explains how to construct an N-layered triangle by adding triangles to an existing triangle to form additional layers. It then presents tables and figures that count the number of upright and inverted trapezoids in each layer of sample N-layered triangles. Using this data, it derives finite difference formulas to calculate the number of upright and inverted trapezoids as functions of N. It combines these formulas to arrive at the final formula: TNT = n(n3 + 35n/4 - n2 - 29) + 33, which calculates the total number ofViewers also liked (10)
7.5 Systems Of Inequalities
7.5 Systems Of Inequalitiesramjdram
Ìý
This document provides instructions for graphing linear inequalities on a coordinate plane. It explains that linear inequalities are graphed as lines but must be shaded according to the inequality sign. To graph an inequality, one must first put it in slope-intercept form, then graph the line as dashed or solid based on the inequality sign, and lastly shade the appropriate region indicated by the inequality sign.System of linear inequalities
System of linear inequalitiesmstf mstf
Ìý
Here is the system of inequalities for the cross-country team problem:
Let x = number of water bottles sold to students
Let y = number of water bottles sold to others
x + y ≤ 100 (they have 100 bottles total)
3x + 5y ≥ 400 (they need at least $400)
Graph the regions defined by these inequalities and the overlapping region is the solution.Linear Equations
Linear Equationsrfant
Ìý
Students learn to define and identify linear equations. They also learn the definition of Standard Form of a linear equation.
Students also learn to graph linear equations using x and y intercepts.Linear equations
Linear equationshireshgupta1997
Ìý
This document discusses linear equations in one variable. It defines linear equations as those involving single variables with the highest power being 1. It presents rules for solving linear equations, including adding, subtracting, multiplying, or dividing the same quantity to both sides. Transposition as a method is explained, where terms change signs when shifted between sides of an equation. Examples of solving linear equations are provided. The document also discusses applying linear equations to word problems by setting up the equation based on the problem and solving for the unknown variable. Several examples of solving word problems involving linear equations are presented.Linear Equation with One Variable (LEOV)
Linear Equation with One Variable (LEOV)SMPK Penabur Gading Serpong
Ìý
1) The document discusses linear equations with one variable (LEOV). It defines key terms like statements, open and closed sentences, equations, and the components of a linear equation with one variable.
2) Examples are provided to illustrate open sentences that can be made into closed sentences or equations by replacing variables with values. Exercises ask the reader to write open sentences as equations and solve simple equations.
3) The final section directs the reader to solve two sample linear equations with one variable, tying together the concepts discussed in the document. Linear Equation In one variable class 7
Linear Equation In one variable class 7Poulami Choudhury
Ìý
This document defines and provides examples of linear equations in one variable. It explains that a linear equation is an equation that can be written in the form ax + b = c or ax = b, where a, b, c are constants and a ≠0. Examples of linear equations given include 3x + 9 = 0 and 7x + 5 = 2x - 9. The document also discusses how to determine if a value is a solution to a linear equation by substitution and simplification. Steps for solving linear equations are provided, which include isolating the variable using inverse operations like addition/subtraction and multiplication/division.linear equation
linear equationkanishkaanandkv
Ìý
1) The document discusses linear equations in two variables, including defining their form as ax + by = c, explaining that they have infinitely many solutions, and noting that their graphs are straight lines.
2) Specific topics covered include finding solutions, drawing graphs, identifying equations for lines parallel to the x-axis and y-axis, and providing examples of writing and solving linear equations.
3) The summary restates the key points about the properties of linear equations in two variables, such as their graphical and algebraic representations.Chapter 3. linear equation and linear equalities in one variables
Chapter 3. linear equation and linear equalities in one variablesmonomath
Ìý
Here are the steps to solve this inequality problem:
1) Write an expression for the perimeter in terms of x
2) Set the perimeter expression ≤ 40
3) Isolate x by undoing the operations
4) Write the solution set
The solution is 0 ≤ x ≤ 7Solution of linear equation & inequality
Solution of linear equation & inequalityDalubhasaan ng Lungsod ng Lucena
Ìý
The document discusses solving linear equalities and inequalities with one variable. It defines key terms like equations, inequalities, and linear equations. It then provides steps for solving different types of linear equations and inequalities by collecting like terms, adding/subtracting the variable term to one side, and multiplying/dividing both sides by constants. The document also explains how to graph solutions to inequalities on a number line, indicating open and closed circles based on the inequality symbols. Examples are provided of solving and graphing various linear equalities and inequalities with one variable.Linear Equations and Inequalities in One Variable
Linear Equations and Inequalities in One Variablemisey_margarette
Ìý
The document discusses linear equations and inequalities in one variable. It defines linear equations and inequalities, and describes methods for solving them including: guess-and-check, cover-up, and working backwards. It also covers properties of equality and inequality, and provides examples of solving linear equations and inequalities using these properties and graphical representations of solution sets on number lines.Similar to Linear Inequalities (10)
Linear Inequality slayerix
Linear Inequality slayerixAshams kurian
Ìý
1) Solving linear inequalities involves using the same concepts as solving linear equations to isolate the variable, but inequalities have infinite solutions rather than a single solution.
2) Inequality signs (<, >, ≤, ≥) indicate whether values are less than, greater than, less than or equal to, or greater than or equal to another value.
3) Graphing linear inequalities on a number line or coordinate plane involves graphing the corresponding equality and then shading the appropriate side based on the inequality sign and whether it includes the endpoint or not.Graphing inequalities in two variables
Graphing inequalities in two variablesJessica Garcia
Ìý
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 ≥.Math Benchmark Part 1
Math Benchmark Part 1Innos
Ìý
An asymptote is a line that a graph approaches but never touches. There are two types of asymptotes: horizontal asymptotes, which are horizontal lines a graph approaches, and vertical asymptotes, which are vertical lines a graph approaches. As a graph gets closer to an asymptote, the space between the graph and asymptote decreases infinitely. Vertical asymptotes occur when factors in the denominator equal zero and do not cancel out factors in the numerator.Graphing sytems inequalities
Graphing sytems inequalitiesJessica Garcia
Ìý
This document provides instructions for graphing systems of linear inequalities:
- Graph each inequality individually by plotting points, drawing the line, and shading the correct region based on whether it is <, ≤, >, or ≥
- Find the overlapping region that satisfies both inequalities, which is the solution to the full system
- An example graphs two inequalities and finds the overlapping purple region as the solution
- Vertices can be found by setting the equations of intersecting lines equal to each otherGraphing inequalities
Graphing inequalitiesmooca76
Ìý
This document discusses how to graph inequalities involving vertical and horizontal lines. It explains that an equation like x=2 graphs as a vertical line where all x values are equal to 2. Inequalities like x≥2 graph the line first and then shade the area indicated by the inequality. Similarly, an equation like y=0 graphs as a horizontal line, and inequalities like y≤0 graph the line and shade the appropriate area. The document also notes that ≤ and ≥ use a solid line when graphing, while > and < use a dotted line. It provides an example of writing a system of inequalities for a solution involving different bounds for x and y values.Graphing sytems inequalities
Graphing sytems inequalitiesJessica Garcia
Ìý
This document provides instructions for graphing systems of linear inequalities. It explains how to write inequalities in slope-intercept form, plot points to draw the line, and shade the appropriate region based on whether it is <, ≤, >, or ≥. An example problem is worked through step-by-step to demonstrate how to graph two inequalities and find the overlapping region that satisfies both inequalities. Practice problems are then provided for the reader to work through on their own.6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variablesguestd1dc2e
Ìý
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.6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variablesguestd1dc2e
Ìý
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.Inequalities powerpoint
Inequalities powerpointrenialumpkin
Ìý
This document provides an introduction to graphing simple inequalities with one variable. It defines an inequality as a statement that two expressions are not equal. It explains the symbols used in inequalities like <, >, ≤, ≥ and how to graph them correctly by using open or closed circles depending on if it is a < or ≤. Examples are provided of graphing different inequalities like x > 3, x < 7, p ≤ -2, and having the reader practice graphing their own inequalities.More from Bitsy Griffin (20)
K 2nd power point animals
K 2nd power point animalsBitsy Griffin
Ìý
This 3 sentence summary provides the essential information from the document in concise form:
The document discusses a PowerPoint presentation that was created using animal pictures from a website. Pictures of animals were posted on the website http://www.shelleypaul.com/animals.html and were used to create the PowerPoint slides. The PowerPoint was made using media from that specific website addressing animal photos.The nine building blocks of civilization
The nine building blocks of civilizationBitsy Griffin
Ìý
Technology advanced in Mesopotamia through irrigation systems, more efficient tools, and the pottery wheel. The Olmec civilization constructed colossal stone heads weighing tons that took thousands to carve, though their purpose remains unclear with multiple interpretations. Laws in early civilizations initially granted women rights but later restricted them, while slavery spread across Mesopotamia and religions influenced behavior through rituals and judgments of the afterlife.Russia
RussiaBitsy Griffin
Ìý
Picture from http://kaitlynnsglobalblog.blogspot.com/. Audio from a Cabarrus County Middle Schooler. 09 19-11 wk 4-1 polygons
09 19-11 wk 4-1 polygonsBitsy Griffin
Ìý
The document discusses identifying and describing polygons. Polygons are classified by the number of sides and angles, and prefixes are used to indicate both the number of sides and angles. The lesson includes creating a bubble map linking polygon prefixes like tri-, quad-, and penta- with the number of sides/angles they represent. Students will assess their understanding by naming polygons using prefix cards and showing the meaning with their fingers.09 20-10 wk 4-2 capacity test
09 20-10 wk 4-2 capacity testBitsy Griffin
Ìý
The document provides instructions for students taking a capacity test. It tells them to get out last week's work, take the test, and continue working on the previous lesson if finished. After the test, students are instructed to review their work and polygon notes. The rotations include the teacher grading tests and multiplication facts, as well as other students working on number forms, stations, puzzles, and math practice.09 22-11 wk4-4 quadrilaterals
09 22-11 wk4-4 quadrilateralsBitsy Griffin
Ìý
The document defines different types of triangles and angles. It then discusses quadrilaterals, identifying them as 4-sided polygons. It defines 5 specific quadrilaterals: parallelograms, rectangles, rhombi, squares, and trapezoids. For each shape, it provides the key attributes like number of parallel sides, angle measures, or side lengths that can be used to identify and describe each quadrilateral. It concludes by instructing the reader to copy a chart with names, drawings and descriptions of quadrilaterals from Buckle Down page 86.09 21-11 wk 4-3 triangle basics
09 21-11 wk 4-3 triangle basicsBitsy Griffin
Ìý
The document discusses identifying and classifying polygons, specifically triangles, based on their sides and angles. It defines different types of angles (right, obtuse, acute, straight) and triangles (scalene, isosceles, equilateral) based on whether their sides and angles are the same or different. The goal is to be able to classify triangles and identify angle types.09 23-11 wk 4-5 volume 2
09 23-11 wk 4-5 volume 2Bitsy Griffin
Ìý
This document discusses finding the volume of rectangular prisms using unit cubes. It explains that a unit cube has edge lengths of 1 and a volume of 1. Students are instructed to build five different rectangular prisms, sketch them, record their volumes, and check each other's work. The teacher's rotations include checking homework, handing out new homework due on 9/30, and having students do more work on finding volume.08 29-10 wk 1-1b place value
08 29-10 wk 1-1b place valueBitsy Griffin
Ìý
This document contains notes from a math lesson on place value. It discusses setting up composition books with title pages, dedications, and tables of contents for note taking. The lesson defines digits and numbers, teaches place value through ordering cards with place value terms, and gives examples of how the digit 9 can be used in different places to change a number's value. Students complete tasks independently in their notebooks to practice reading and understanding place value.08 26-11 wk 1-1 problem solving
08 26-11 wk 1-1 problem solvingBitsy Griffin
Ìý
The document outlines an 8th grade classroom lesson plan on problem solving. It includes introducing problem solving strategies and having students practice using strategies like creating Venn diagrams to compare two approaches. Students also identify operational words and work on a Sudoku problem in groups. The lesson aims to help students understand different methods for solving problems.Math vocabulary 5th NC
Math vocabulary 5th NCBitsy Griffin
Ìý
The document provides definitions and examples for various math terms related to numbers, operations, measurement, geometry, and problem solving strategies. It includes 3 or fewer sentence summaries of rational numbers, place value, ordering numbers, estimating, factors and multiples, equivalence, symbols for relationships, fractions, decimals, angles, shapes, and units of measurement. Visual examples and links are provided with several terms.12 3-10 circle graphs
12 3-10 circle graphsBitsy Griffin
Ìý
The document contains notes from a data collection session on reading circle graphs. It includes definitions of key circle graph terms like wedges and percentages represented as decimals. Examples are provided for calculating percentages of a total number and converting between percentages, fractions, and decimals. Students are assigned practice problems working with circle graphs.Dewey decimal classification system
Dewey decimal classification systemBitsy Griffin
Ìý
Melvil Dewey created the Dewey Decimal Classification (DDC) system when he was 21 years old to bring order to the organization of books in libraries. The DDC system divides all knowledge into 10 main categories, with each category represented by 3 numbers. These numbers can be found on the spine of each library book and help library patrons easily locate books on the shelves. The 10 main categories include generalities, philosophy, religion, social science, language, science and math, technology, arts, literature, and geography and history.Wk 4 1 polygon classification
Wk 4 1 polygon classificationBitsy Griffin
Ìý
Polygons are classified based on the number of sides and angles they have. Prefixes are used to indicate the number of sides, for example "tri" means 3 sides. A bubble map shows common polygons such as triangles, quadrilaterals, pentagons, hexagons, etc. and their corresponding prefixes and number of sides.Measurement Review
Measurement ReviewBitsy Griffin
Ìý
This document discusses different measurement systems and how to convert between them. It covers the metric and customary systems for measuring mass, weight, length, and capacity/volume. The metric system uses multiples of 10, while the customary system's units vary. Conversion factors are provided, such as 16 ounces in a pound or 128 ounces in a gallon. The document aims to explain the different units and how to convert between metric and customary measurements.2 30 Data Collection
2 30 Data CollectionBitsy Griffin
Ìý
This document discusses various methods for collecting and displaying data, including frequency tables, line plots, bar graphs, picture graphs, line graphs, stem-and-leaf plots, histograms, and circle graphs. It also explains how to calculate the mean, median, mode, and range of a data set by adding and dividing numbers, ordering values, identifying the middle number, finding the most frequent number, and subtracting the smallest number from the largest number.Organism Diversity in Ecosystems
Organism Diversity in EcosystemsBitsy Griffin
Ìý
Organisms diversify in an ecosystem by occupying different niches. An ecosystem can support many populations of different species because each population uses the ecosystem's resources in different ways. Populations are made up of the same species living in the same habitat. Multiple populations together make up the community of organisms in an ecosystem. Organisms avoid competition by occupying different niches defined by factors like habitat, food sources, behaviors, and activity times.2 28 Add Subtract Decimals
2 28 Add Subtract DecimalsBitsy Griffin
Ìý
The document provides guidance on adding and subtracting decimals. It recommends lining up the decimals on top of each other and filling in zeros as placeholders when the numbers of decimals do not match up. Examples are provided of adding 8.23 + 4.65 and subtracting 3.6 - 1.042. Practice problems are assigned from various pages and the answers to the practice problems are provided.2 25 Adding Subtracting Mixed Numbers
2 25 Adding Subtracting Mixed NumbersBitsy Griffin
Ìý
This document provides guidance on adding and subtracting mixed numbers. It begins with reviewing how to add and subtract fractions with the same or different denominators. It then works through 4 example problems step-by-step, showing how to rename mixed numbers if needed so the fractions have a common denominator before adding or subtracting. The key steps are to rename any mixed numbers, find a common denominator for the fractions, then add or subtract the whole numbers and fractions.2 24 Adding & Subtracting Fractions With Unlike Denominators
2 24 Adding & Subtracting Fractions With Unlike DenominatorsBitsy Griffin
Ìý
This document provides examples for adding and subtracting fractions with unlike denominators. It explains that to add fractions with different denominators, you must first find the least common denominator and convert the fractions so they have the same denominator. Then you can simply add the numerators and keep the common denominator. Subtraction follows the same process. Several word problems are worked through step-by-step as examples.Linear Inequalities
- 2. Background How do you graph x < 1 on the number line?
- 3. Background On the coordinate plane, x < 1 is graphed like this:
- 4. Background For inequalities on the coordinate plane: < & > are represented with a dashed line ≤ & ≥ are represented with a solid line (non-dashed line)
- 5. x without y x > # x ≤ #
- 6. y without x y > # y ≤ #
- 7. Linear Inequalities Make sure the inequality is in slope intercept form. All the rules you know about inequalities apply here: If you multiply or divide by a negative number you have to flip the sign.
- 8. Linear Inequalities After the equation is in slope intercept form, graph the line. Use a dashed line if the sign is < or >. The big thing is, understanding where to shade. The sign helps you know where to shade.
- 9. Linear Inequalities y > will be shaded toward the top of the graph
- 10. Linear Inequalities y < will be shaded toward the bottom of the graph
- 11. Linear Inequalities y < will be shaded toward the bottom of the graph
- 12. Linear Inequalities Since every graph lays on the coordinate plane differently, toward the top and toward the bottom is a bit subjective. The best way to get a good feel for it is to work a lot of problems.