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This document discusses using the two-point form to find the equation of a line given two points. It provides the two-point form equation, examples of using the form to find the slope and y-intercept of lines, and practice problems for determining the equation of lines passing through two points. The goal is to determine the equation in slope-intercept form using the two-point form equation and substituting the x- and y-coordinates of the two points.

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System of Linear inequalities in two variables

This document provides instructions for solving systems of linear inequalities in two variables by graphing. It defines a system of inequalities and explains that the solution is the region where the graphs of the inequalities overlap. A step-by-step process is outlined: 1) graph each inequality individually, 2) shade the appropriate half-plane, 3) the overlapping shaded regions represent the solution. An example system is graphed to demonstrate. Students will evaluate by being assigned a system to graph and answer related questions about the solution region.

Factoring Sum and Difference of Two Cubes

This will help you in factoring sum and difference of two cubes.
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Solving quadratics by completing the square

The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Additional examples demonstrate applying these steps to solve quadratic equations algebraically.

Illustrations of Quadratic Equations

You will learn how to get the value of a, b and c given a quadratic equations.
For more instructional resources, CLICK me here! 👇👇👇
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https://tinyurl.com/ycjp8r7u
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Math 8 - Linear Inequalities in Two Variables

This document is a math lesson plan on linear inequalities in two variables taught by Mr. Carlo Justino J. Luna at Malabanias Integrated School in Angeles City. The lesson introduces linear inequalities and their notation, defines them as having two linear expressions separated by symbols like greater than and less than, and shows examples of inequalities in two variables. It then discusses how to determine if an ordered pair is a solution by substituting into the inequality. Finally, it explains how to graph linear inequalities in two variables by first rewriting them as equations and then plotting intercepts and shading the appropriate region based on a test point.

Illustrating Rational Algebraic Expressions

If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
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two intercept form

The document discusses using the two intercept form to find the equation of a line given two points. It provides the two intercept form equation, where a and b are the x and y intercepts. It then works through three examples of finding the line equation using two points and the two intercept form. It lists additional practice problems and their solutions for finding line equations using two points and the two intercept form.

Factoring Polynomials

This document provides instructions on factoring polynomials of various forms:
1) It explains how to factor polynomials by finding the greatest common factor (GCF).
2) It describes how to factor trinomials of the form x2 + bx + c by finding two numbers whose sum is b and product is c.
3) It shows how to factor trinomials of the form ax2 + bx + c by finding factors of a, c whose products and sums satisfy the polynomial.

System of Linear inequalities in two variables

This document provides instructions for solving systems of linear inequalities in two variables by graphing. It defines a system of inequalities and explains that the solution is the region where the graphs of the inequalities overlap. A step-by-step process is outlined: 1) graph each inequality individually, 2) shade the appropriate half-plane, 3) the overlapping shaded regions represent the solution. An example system is graphed to demonstrate. Students will evaluate by being assigned a system to graph and answer related questions about the solution region.

Factoring Sum and Difference of Two Cubes

This will help you in factoring sum and difference of two cubes.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

Solving quadratics by completing the square

The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Additional examples demonstrate applying these steps to solve quadratic equations algebraically.

Illustrations of Quadratic Equations

You will learn how to get the value of a, b and c given a quadratic equations.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

Math 8 - Linear Inequalities in Two Variables

This document is a math lesson plan on linear inequalities in two variables taught by Mr. Carlo Justino J. Luna at Malabanias Integrated School in Angeles City. The lesson introduces linear inequalities and their notation, defines them as having two linear expressions separated by symbols like greater than and less than, and shows examples of inequalities in two variables. It then discusses how to determine if an ordered pair is a solution by substituting into the inequality. Finally, it explains how to graph linear inequalities in two variables by first rewriting them as equations and then plotting intercepts and shading the appropriate region based on a test point.

Illustrating Rational Algebraic Expressions

If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

two intercept form

The document discusses using the two intercept form to find the equation of a line given two points. It provides the two intercept form equation, where a and b are the x and y intercepts. It then works through three examples of finding the line equation using two points and the two intercept form. It lists additional practice problems and their solutions for finding line equations using two points and the two intercept form.

Factoring Polynomials

This document provides instructions on factoring polynomials of various forms:
1) It explains how to factor polynomials by finding the greatest common factor (GCF).
2) It describes how to factor trinomials of the form x2 + bx + c by finding two numbers whose sum is b and product is c.
3) It shows how to factor trinomials of the form ax2 + bx + c by finding factors of a, c whose products and sums satisfy the polynomial.

Combined Variation

This document discusses combined variation and how to solve problems involving quantities that vary directly and inversely with other variables. It provides examples of translating statements of combined variation into mathematical equations. It also works through an example problem, showing how to solve for an unknown variable value when the quantities it varies with are given. The document concludes by instructing the reader to practice additional combined variation problems from their workbook.

Direct Variation

Direct variation describes the relationship between two quantities where one quantity varies as the other changes proportionally. It can be represented by the equation y = kx, where k is the constant of variation.
Some key points about direct variation:
- The graph of a direct variation will pass through the origin, as there is no y-intercept term.
- To determine if a relationship represents direct variation, calculate the constant of variation k from the data and check if it remains the same for different values.
- Direct variation can be used to find unknown values by setting up a table with the known values and using the direct variation equation y = kx.

Factoring Perfect Square Trinomial

The document discusses factoring perfect square trinomials (polynomials with three terms where the first and last terms are perfect squares). It provides examples of factoring expressions like x^2 + 8x + 16 into (x + 4)^2. For an expression to be a perfect square trinomial, the first term must be a perfect square, the third term must be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms. Students are provided examples and exercises to practice factoring various square trinomial expressions.

Factoring Polynomials

This document discusses various methods for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF) of terms in a polynomial.
2) Factoring trinomials of the form x^2 + bx + c by finding two numbers whose product is c and sum is b.
3) Factoring polynomials using grouping when the GCF is not a single term.
4) Recognizing perfect square trinomials and factoring using (a + b)^2 = a^2 + 2ab + b^2.

Graphing polynomial functions (Grade 10)

This document provides instructions on graphing polynomial functions. It discusses identifying the roots, x-intercepts, and y-intercept from the factored form of the polynomial. It shows working through an example of graphing the function y = (x – 2)(x – 1)(x + 3). The key steps are:
1. Identify the roots and y-intercept
2. Arrange the roots in a table
3. Complete the table by calculating y-values for different x-values
4. Plot the points on a graph
5. Sketch the graph

Factoring the Sum and Difference of Two Cubes Worksheet

This document contains a mathematics worksheet for 8th grade algebra students. It provides instructions on factoring the sum and difference of two cubes using steps such as identifying common factors, taking cube roots, and forming trinomial expressions. The worksheet then lists 14 practice problems for students to factor expressions involving sums and differences of cubes.

Solving Systems of Linear Equations in Two Variables by Graphing

This document discusses solving systems of linear equations in two variables by graphing. It begins by recalling the different types of systems and their properties. It then shows examples of writing linear equations in slope-intercept form and graphing individual equations. The main steps for solving a system by graphing are outlined: 1) write both equations in slope-intercept form, 2) graph them on the same plane, 3) find the point of intersection, and 4) check that the solution satisfies both equations. Several examples are worked through demonstrating how to graph systems, find the point of intersection, and verify the solution. The document concludes with an application problem asking students to solve systems, identify the solution location on a map, and describe the

Factoring Perfect Square Trinomials Worksheet

This document is a mathematics worksheet on algebra that provides instructions on factoring perfect square trinomials. It explains that recognizing the pattern of perfect squares can save time on tests. The pattern is to take the square roots of the first and last terms and place them in parentheses with a plus or minus between them, then square the whole expression. Examples of factoring expressions using this pattern are provided.

Direct variation power point

The document defines direct variation and provides examples of how to determine if a relationship is direct variation. It explains that direct variation can be represented by an equation in the form of y=kx, where k is the constant of variation. It gives examples of determining the constant of variation from tables of x and y values and using the constant to find unknown values. It also provides examples of solving word problems using direct variation.

Rational Expressions

To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
x^2(x-5)(x-6) = x^2(x-5)(x-6)
Canceling the common factors, we obtain:
x^2 = x^2
Since this holds for all real values of x, the solution is all real numbers. Therefore, the solution is x ∈ R.

Angles Formed by Parallel Lines Cut by a Transversal

This document discusses parallel lines and angles formed when lines are cut by a transversal. It begins by defining parallel lines and explaining that a transversal is a line that intersects two or more lines at different points. It then defines and provides examples of several types of angles formed, including alternate interior/exterior angles, same side interior/exterior angles, and corresponding angles. Groups are then assigned to prove properties of these angles for parallel lines cut by a transversal. The document concludes with practice problems finding missing angle measures using the properties and an assignment involving parallel lines cut by a transversal.

Solving problems involving linear inequalities in two variables

This document discusses solving problems involving linear inequalities in two variables. It begins by stating the learning objectives, which are to solve such problems and appreciate their use in real-life situations. An activity is presented involving using a budget to purchase ingredients for chicken adobo. Students are asked to model word problems using linear inequalities with two variables. Examples are provided and students practice translating situations into inequalities. The document solves sample problems and discusses using inequalities to represent real-life scenarios. Students are ultimately tasked with finding examples of such situations from their own experiences.

Equations of a Line

This document provides instruction on writing equations of lines using different forms: slope-intercept, point-slope, two-point, and intercept forms. Examples are given for writing equations of lines when given characteristics like slope, points, or intercepts. The last section presents an application example of using line equations to determine if two sets of bones found in an excavation site are parallel.

Solving Equations Involving Radical Expressions

This document discusses how to solve radical equations by isolating the radical expression, removing the radical sign by raising both sides to the appropriate power, and solving the resulting equation. It provides examples of solving various radical equations step-by-step and checking solutions. Key steps include isolating the radical term, removing the radical, solving the resulting equation, and checking for extraneous roots.

Simplifying Rational Algebraic Expressions

If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

Factoring the Common Monomial Factor Worksheet

This document is a mathematics worksheet for 8th grade algebra covering factoring expressions. It contains 22 problems of varying difficulty ranging from easy single term factoring to harder multi-term expressions. The problems are grouped into three sections: Easy, Average, and Hard. For each problem, the factors of the expression are provided as the answer. No other context is given around the worksheet such as the purpose, learning objectives, or how it fits into the curriculum.

Multiplying & dividing rational algebraic expressions

This document discusses how to multiply and divide rational algebraic expressions. It explains that to multiply rational expressions, one multiplies the numerators and denominators separately. Rational expressions must first be factored to cancel common factors before multiplying. Several examples of multiplying rational expressions are shown. The document also explains that to divide rational expressions, one multiplies the numerator by the reciprocal of the denominator. Some examples of dividing rational expressions are provided.

Math 8 - Linear Functions

This document discusses linear functions and how to represent them using equations, graphs, and tables of values. It defines a linear function as one that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. Examples are provided to illustrate determining the slope and y-intercept from an equation and representing a linear function using an equation, table of values, or graph. It is explained that a linear function will produce a straight line on a graph and have constant differences in x- and y-coordinates in its table of values.

Solving Quadratic Equations by Factoring

This document provides examples for solving quadratic equations by factoring. It explains how to solve equations of the form ax^2 + bx = 0 and ax^2 + bx + c = 0 by factoring and setting each factor equal to zero. Some example problems are worked out step-by-step, including solving 11x^2 - 13x = 8x - 3x^2 and 7x^2 + 18x = 10x^2 + 12x. The document also discusses using the fact that the roots of ax^2 + bx = 0 are x = 0 and x = -b/a to solve equations without factoring. It concludes by explaining how to use the zero product property to solve a quadratic

System of linear inequalities

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.

point slope form

This document discusses using the point-slope form to find the equation of a line given a slope and point. It provides the point-slope form equation, and examples of finding the line equation for different slopes and points. Exercises are provided for the reader to practice finding additional line equations using given slopes and points.

Equation Of A Line

This document discusses different methods for finding the equation of a line, including:
1) Given the slope and y-intercept
2) Using a graph
3) Given a point and the slope
4) Given two points
It provides examples of how to write the line equation using each method.

Combined Variation

This document discusses combined variation and how to solve problems involving quantities that vary directly and inversely with other variables. It provides examples of translating statements of combined variation into mathematical equations. It also works through an example problem, showing how to solve for an unknown variable value when the quantities it varies with are given. The document concludes by instructing the reader to practice additional combined variation problems from their workbook.

Direct Variation

Direct variation describes the relationship between two quantities where one quantity varies as the other changes proportionally. It can be represented by the equation y = kx, where k is the constant of variation.
Some key points about direct variation:
- The graph of a direct variation will pass through the origin, as there is no y-intercept term.
- To determine if a relationship represents direct variation, calculate the constant of variation k from the data and check if it remains the same for different values.
- Direct variation can be used to find unknown values by setting up a table with the known values and using the direct variation equation y = kx.

Factoring Perfect Square Trinomial

The document discusses factoring perfect square trinomials (polynomials with three terms where the first and last terms are perfect squares). It provides examples of factoring expressions like x^2 + 8x + 16 into (x + 4)^2. For an expression to be a perfect square trinomial, the first term must be a perfect square, the third term must be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms. Students are provided examples and exercises to practice factoring various square trinomial expressions.

Factoring Polynomials

This document discusses various methods for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF) of terms in a polynomial.
2) Factoring trinomials of the form x^2 + bx + c by finding two numbers whose product is c and sum is b.
3) Factoring polynomials using grouping when the GCF is not a single term.
4) Recognizing perfect square trinomials and factoring using (a + b)^2 = a^2 + 2ab + b^2.

Graphing polynomial functions (Grade 10)

This document provides instructions on graphing polynomial functions. It discusses identifying the roots, x-intercepts, and y-intercept from the factored form of the polynomial. It shows working through an example of graphing the function y = (x – 2)(x – 1)(x + 3). The key steps are:
1. Identify the roots and y-intercept
2. Arrange the roots in a table
3. Complete the table by calculating y-values for different x-values
4. Plot the points on a graph
5. Sketch the graph

Factoring the Sum and Difference of Two Cubes Worksheet

This document contains a mathematics worksheet for 8th grade algebra students. It provides instructions on factoring the sum and difference of two cubes using steps such as identifying common factors, taking cube roots, and forming trinomial expressions. The worksheet then lists 14 practice problems for students to factor expressions involving sums and differences of cubes.

Solving Systems of Linear Equations in Two Variables by Graphing

This document discusses solving systems of linear equations in two variables by graphing. It begins by recalling the different types of systems and their properties. It then shows examples of writing linear equations in slope-intercept form and graphing individual equations. The main steps for solving a system by graphing are outlined: 1) write both equations in slope-intercept form, 2) graph them on the same plane, 3) find the point of intersection, and 4) check that the solution satisfies both equations. Several examples are worked through demonstrating how to graph systems, find the point of intersection, and verify the solution. The document concludes with an application problem asking students to solve systems, identify the solution location on a map, and describe the

Factoring Perfect Square Trinomials Worksheet

This document is a mathematics worksheet on algebra that provides instructions on factoring perfect square trinomials. It explains that recognizing the pattern of perfect squares can save time on tests. The pattern is to take the square roots of the first and last terms and place them in parentheses with a plus or minus between them, then square the whole expression. Examples of factoring expressions using this pattern are provided.

Direct variation power point

The document defines direct variation and provides examples of how to determine if a relationship is direct variation. It explains that direct variation can be represented by an equation in the form of y=kx, where k is the constant of variation. It gives examples of determining the constant of variation from tables of x and y values and using the constant to find unknown values. It also provides examples of solving word problems using direct variation.

Rational Expressions

To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
x^2(x-5)(x-6) = x^2(x-5)(x-6)
Canceling the common factors, we obtain:
x^2 = x^2
Since this holds for all real values of x, the solution is all real numbers. Therefore, the solution is x ∈ R.

Angles Formed by Parallel Lines Cut by a Transversal

This document discusses parallel lines and angles formed when lines are cut by a transversal. It begins by defining parallel lines and explaining that a transversal is a line that intersects two or more lines at different points. It then defines and provides examples of several types of angles formed, including alternate interior/exterior angles, same side interior/exterior angles, and corresponding angles. Groups are then assigned to prove properties of these angles for parallel lines cut by a transversal. The document concludes with practice problems finding missing angle measures using the properties and an assignment involving parallel lines cut by a transversal.

Solving problems involving linear inequalities in two variables

This document discusses solving problems involving linear inequalities in two variables. It begins by stating the learning objectives, which are to solve such problems and appreciate their use in real-life situations. An activity is presented involving using a budget to purchase ingredients for chicken adobo. Students are asked to model word problems using linear inequalities with two variables. Examples are provided and students practice translating situations into inequalities. The document solves sample problems and discusses using inequalities to represent real-life scenarios. Students are ultimately tasked with finding examples of such situations from their own experiences.

Equations of a Line

This document provides instruction on writing equations of lines using different forms: slope-intercept, point-slope, two-point, and intercept forms. Examples are given for writing equations of lines when given characteristics like slope, points, or intercepts. The last section presents an application example of using line equations to determine if two sets of bones found in an excavation site are parallel.

Solving Equations Involving Radical Expressions

This document discusses how to solve radical equations by isolating the radical expression, removing the radical sign by raising both sides to the appropriate power, and solving the resulting equation. It provides examples of solving various radical equations step-by-step and checking solutions. Key steps include isolating the radical term, removing the radical, solving the resulting equation, and checking for extraneous roots.

Simplifying Rational Algebraic ExpressionsIf you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

Factoring the Common Monomial Factor Worksheet

This document is a mathematics worksheet for 8th grade algebra covering factoring expressions. It contains 22 problems of varying difficulty ranging from easy single term factoring to harder multi-term expressions. The problems are grouped into three sections: Easy, Average, and Hard. For each problem, the factors of the expression are provided as the answer. No other context is given around the worksheet such as the purpose, learning objectives, or how it fits into the curriculum.

Multiplying & dividing rational algebraic expressions

This document discusses how to multiply and divide rational algebraic expressions. It explains that to multiply rational expressions, one multiplies the numerators and denominators separately. Rational expressions must first be factored to cancel common factors before multiplying. Several examples of multiplying rational expressions are shown. The document also explains that to divide rational expressions, one multiplies the numerator by the reciprocal of the denominator. Some examples of dividing rational expressions are provided.

Math 8 - Linear Functions

This document discusses linear functions and how to represent them using equations, graphs, and tables of values. It defines a linear function as one that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. Examples are provided to illustrate determining the slope and y-intercept from an equation and representing a linear function using an equation, table of values, or graph. It is explained that a linear function will produce a straight line on a graph and have constant differences in x- and y-coordinates in its table of values.

Solving Quadratic Equations by Factoring

This document provides examples for solving quadratic equations by factoring. It explains how to solve equations of the form ax^2 + bx = 0 and ax^2 + bx + c = 0 by factoring and setting each factor equal to zero. Some example problems are worked out step-by-step, including solving 11x^2 - 13x = 8x - 3x^2 and 7x^2 + 18x = 10x^2 + 12x. The document also discusses using the fact that the roots of ax^2 + bx = 0 are x = 0 and x = -b/a to solve equations without factoring. It concludes by explaining how to use the zero product property to solve a quadratic

System of linear inequalities

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.

Combined Variation

Combined Variation

Direct Variation

Direct Variation

Factoring Perfect Square Trinomial

Factoring Perfect Square Trinomial

Factoring Polynomials

Factoring Polynomials

Graphing polynomial functions (Grade 10)

Graphing polynomial functions (Grade 10)

Factoring the Sum and Difference of Two Cubes Worksheet

Factoring the Sum and Difference of Two Cubes Worksheet

Solving Systems of Linear Equations in Two Variables by Graphing

Solving Systems of Linear Equations in Two Variables by Graphing

Factoring Perfect Square Trinomials Worksheet

Factoring Perfect Square Trinomials Worksheet

Direct variation power point

Direct variation power point

Rational Expressions

Rational Expressions

Angles Formed by Parallel Lines Cut by a Transversal

Angles Formed by Parallel Lines Cut by a Transversal

Solving problems involving linear inequalities in two variables

Solving problems involving linear inequalities in two variables

Equations of a Line

Equations of a Line

Solving Equations Involving Radical Expressions

Solving Equations Involving Radical Expressions

Simplifying Rational Algebraic Expressions

Simplifying Rational Algebraic Expressions

Factoring the Common Monomial Factor Worksheet

Factoring the Common Monomial Factor Worksheet

Multiplying & dividing rational algebraic expressions

Multiplying & dividing rational algebraic expressions

Math 8 - Linear Functions

Math 8 - Linear Functions

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring

System of linear inequalities

System of linear inequalities

point slope form

This document discusses using the point-slope form to find the equation of a line given a slope and point. It provides the point-slope form equation, and examples of finding the line equation for different slopes and points. Exercises are provided for the reader to practice finding additional line equations using given slopes and points.

Equation Of A Line

This document discusses different methods for finding the equation of a line, including:
1) Given the slope and y-intercept
2) Using a graph
3) Given a point and the slope
4) Given two points
It provides examples of how to write the line equation using each method.

Alg. 1 day 60 6 4 point slope form

The document discusses point-slope form of linear equations. It provides examples of writing equations in point-slope form given a slope and point, as well as graphing lines from their point-slope form equations. Key aspects include using the difference in y-values as the slope times the difference in x-values, and substituting the point's x- and y-values and given slope into the point-slope form equation y - y1 = m(x - x1).

chapter1_part2.pdf

1. This document discusses linear equations, slope, graphing lines, writing equations in slope-intercept form, and solving systems of linear equations.
2. Key concepts explained include slope as rise over run, the different forms of writing a linear equation, finding the x- and y-intercepts, and using two points to write the equation of a line in slope-intercept form.
3. Examples are provided to demonstrate how to graph lines based on their equations in different forms, find intercepts, write equations from two points, and solve systems of linear equations.

February 18 2016

The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a known point on the line and m is the slope.
- Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0.
It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting between

6.4_standard_form.ppt

1. The document provides examples of writing linear equations in slope-intercept form, point-slope form, and standard form. It also includes examples of finding the slope and y-intercept of a line from its graph and writing equations of lines given certain points on the line.
2. There are guided practice problems that have students write equations of lines passing through given points, with one point and the slope given, and finding missing coefficients in standard form equations.
3. The examples and guided practice cover skills related to writing, manipulating, and identifying components of linear equations.

Finding Equation of a Line.pptx

This document discusses different forms of linear functions and provides examples of determining the equation of a line given certain information. It introduces four forms of a linear function: slope-intercept form, standard form, point-slope form, and intercept form. It then gives three examples of finding the equation of a line using different forms, given the slope, two points on the line, or the x- and y-intercepts.

Linear Equations in Two Variables.pptx

The document discusses linear equations in two variables. It will cover writing linear equations in standard and slope-intercept form, graphing linear equations using two points, intercepts and slope/point, and describing graphs by their intercepts and slope. Key topics include defining the standard form as Ax + By = C, rewriting equations between the two forms, using two points, x-intercept, y-intercept or slope/point to graph, and describing graphs by their slope and intercepts.

WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx

The document discusses linear equations and graphing linear relationships. It defines key terms like slope, y-intercept, x-intercept, and provides examples of writing linear equations in slope-intercept form and point-slope form given certain information like a point and slope. It also discusses using tables and graphs to plot linear equations and find slopes from graphs or between two points. Real-world examples of linear relationships are provided as well.

TechMathI - Point slope form

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The document discusses key concepts in coordinate geometry including:
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2 3 Bzca5e

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3. Linear equations can be written in slope-intercept form y = mx + b or point-slope form y - y1 = m(x - x1) to graph the line.
4. Parallel lines have the same slope while perpendicular lines have slopes that are negative reciprocals.

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The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
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Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
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The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
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- 1. EQUATION OF THE LINE USING TWO POINT FORM
- 2. Jessebel G. Bautista Antonio J. Villegas Voc’l High School My Profile
- 3. OBJECTIVES: 1.determine the values of the variables 2.use two point form 3.substitute the given values 4.find the equation of a line
- 4. Mathematical Concepts: Two Intercept Form where a and b are x and y intercepts of the line respectively. 𝑥 𝑎 + 𝑦 𝑏 = 1
- 5. Mathematical Concepts: The Point-Slope Form given a slope and a point of a line, we may find the equation by substituting their respective values in the point-slope form. y - y1 = m (x - x1)
- 6. Mathematical Concepts: The Two-Point Form given two points of a line determine the values of x1, y1, x2, and y2 then substitute it to the two-point form to find the equation of the line. y - y1 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (x - x1)
- 7. EXAMPLE 1 1. (8, 5), (6, 1) Solution: Let x1 = 8 x2 = 6 y1 = 5 y2 = 1 Substitute assigned values to the two-point form. Find the equation of a line that passes through the following points. Express the equation in the slope-intercept form. y - 5 = 1−5 6−8 (x - 8) y - 5 = −4 −2 (x - 8) y - 5 = 2(x - 8) y - 5 = 2x - 16 y = 2x -11 y - y1 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (x - x1)
- 8. EXAMPLE 2 2. (5, 6), (7, -4) Solution: Let x1 = 5 x2 = 7 y1 = 6 y2 = -4 Substitute assigned values to the two-point form. Find the equation of a line that passes through the following points. Express the equation in the slope-intercept form. y - 6 = −4−6 7−5 (x - 5) y - 6 = −10 2 (x - 5) y - 6 = -5(x - 5) y - 6 = -5x + 25 y = -5x + 31 y - y1 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (x - x1)
- 9. EXAMPLE 3 3. (5, 3), (3, 1) Solution: Let x1 = 5 x2 = 3 y1 = 3 y2 = 1 Substitute assigned values to the two-point form. Find the equation of a line that passes through the following points. Express the equation in the slope-intercept form. y - 5 = 1−3 3−5 (x - 5) y - 5 = −2 −2 (x - 5) y - 5 = 1(x - 5) y - 5 = x - 5 y = x + 0 y = x y - y1 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (x - x1)
- 10. TO DO … 1. (9,6) & (7, -5) 2. (0,3) & (1,0) 3. (4,3) & (2,1) 4. (-7, 1) & (1, -3) 5. ( 4, -3) & (-2, 1) 6. (8, 6) & (8, -3) 7. ( -5, 1) & (-6 , 4) 8. (11, -7) & (6, -9) 9. (-6, -4) & (-10, -2) 10. (4, -6) & (1, -6) Find the equation of the line that passes through the following given points. Express the equation in slope-intercept form.
- 11. SALAMAT PO!!!
- 12. Learning Resources: Grade 8 Math Time k-to-12-grade-8-math-learner-module Learning Resources: