Slope
•Download as PPTX, PDF•
0 likes•235 views
The document discusses finding the slope of a line by using the formula slope = (y2 - y1) / (x2 - x1). It provides an example of using the formula to find the slope from the coordinates (2,2) and (5,1), which is (2 - 1) / (5 - 2) = 1/-3. The document encourages the reader to memorize the slope formula as it makes finding slopes easy once learned.
Report
Share
Report
Share
Recommended
Lsn 12 6
This document contains a graph with labeled x and y axes ranging from -6 to 6. Within this range are curved lines forming a circle centered at the point (4, 1).
Interesting Mathematics2- Belgium
To draw a parabolic dome with a radius of 6m and height of 3.6m:
1) The equation of the parabola is y = (x^2)/10 - 2.5, with a focus of (0, 2.5) and directrix of y = -2.5.
2) Plot the directrix and focus, then draw parabolic arcs above the directrix using the focus to define the curve.
Week 13
This document contains notes from multiple days of function lessons. It includes examples of functions in standard form and their x-intercepts and y-intercepts. It also gives practice problems finding outputs of functions like f(x) = 2x - 5 for various inputs. The notes describe setting up function stations to practice notation, the vertical line test, real-world illustrations, domains and ranges. It concludes with reminders about an upcoming quiz on functions and making up any missed work.
MATHS SYMBOLS - ROOTS - #2 - PROPERTIES 0 - 2A
ROOTS - PROPERTIES 0, 1, 1A, 1B, 1C, 1D, 2, 2A
- ROOTS and THEIR PROPERTIES
- 10+ PROPERTIES
- RATIONALISING the DENOMINATOR
- RADICAL EQUATION
- PROOFS, EXAMPLES
- CALCULATIONS STEP by STEP
MATHS SYMBOLS
www.enzoexposito.it/mobile/matematica.html
www.enzoexposito.it/mobile/aritmetica.html
5.1 Finding Slope
The student will learn to find the slope of a line given two points or a graph. Slope represents the steepness of a line and can be calculated using the formula of rise over run or by using the points in the slope formula. Horizontal lines have a slope of 0 and vertical lines have an undefined slope. The document provides examples of finding the slope of lines from graphs and points.
Descgeom 02 locating points in space
The document discusses various concepts in descriptive geometry related to locating points and lines in space. It provides instructions on how to determine the missing projection of a point given two other projections, how to project a line into other views, and how to determine the relative positions of points based on their projections. It includes examples of problems asking to locate points or complete views based on given positional descriptions and provides instructions for seatwork problems to practice these concepts.
1539 graphs linear equations and functions
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Prove It!
The document discusses geometry proofs, including givens and conclusions, triangle congruencies, triangle congruency shortcuts using SSS, SAS, ASA, AAS, and HL, writing two-column proofs, and applying the CPCTC principle that corresponding parts of congruent triangles are congruent. It provides examples of two-column proofs using different congruency rules and reasoning to prove that two triangles are congruent.
Recommended
Lsn 12 6
This document contains a graph with labeled x and y axes ranging from -6 to 6. Within this range are curved lines forming a circle centered at the point (4, 1).
Interesting Mathematics2- Belgium
To draw a parabolic dome with a radius of 6m and height of 3.6m:
1) The equation of the parabola is y = (x^2)/10 - 2.5, with a focus of (0, 2.5) and directrix of y = -2.5.
2) Plot the directrix and focus, then draw parabolic arcs above the directrix using the focus to define the curve.
Week 13
This document contains notes from multiple days of function lessons. It includes examples of functions in standard form and their x-intercepts and y-intercepts. It also gives practice problems finding outputs of functions like f(x) = 2x - 5 for various inputs. The notes describe setting up function stations to practice notation, the vertical line test, real-world illustrations, domains and ranges. It concludes with reminders about an upcoming quiz on functions and making up any missed work.
MATHS SYMBOLS - ROOTS - #2 - PROPERTIES 0 - 2A
ROOTS - PROPERTIES 0, 1, 1A, 1B, 1C, 1D, 2, 2A
- ROOTS and THEIR PROPERTIES
- 10+ PROPERTIES
- RATIONALISING the DENOMINATOR
- RADICAL EQUATION
- PROOFS, EXAMPLES
- CALCULATIONS STEP by STEP
MATHS SYMBOLS
www.enzoexposito.it/mobile/matematica.html
www.enzoexposito.it/mobile/aritmetica.html
5.1 Finding Slope
The student will learn to find the slope of a line given two points or a graph. Slope represents the steepness of a line and can be calculated using the formula of rise over run or by using the points in the slope formula. Horizontal lines have a slope of 0 and vertical lines have an undefined slope. The document provides examples of finding the slope of lines from graphs and points.
Descgeom 02 locating points in space
The document discusses various concepts in descriptive geometry related to locating points and lines in space. It provides instructions on how to determine the missing projection of a point given two other projections, how to project a line into other views, and how to determine the relative positions of points based on their projections. It includes examples of problems asking to locate points or complete views based on given positional descriptions and provides instructions for seatwork problems to practice these concepts.
1539 graphs linear equations and functions
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Prove It!
The document discusses geometry proofs, including givens and conclusions, triangle congruencies, triangle congruency shortcuts using SSS, SAS, ASA, AAS, and HL, writing two-column proofs, and applying the CPCTC principle that corresponding parts of congruent triangles are congruent. It provides examples of two-column proofs using different congruency rules and reasoning to prove that two triangles are congruent.
6 1 coordinate proofs
Analytic geometry uses algebraic methods to study and prove geometric problems using coordinates. This chapter discusses using coordinate proofs to prove theorems from geometry. It provides instructions on how to construct a coordinate proof by drawing and labeling a diagram, listing given information, stating what will be proved, using algebra to add to the diagram and prove the statement, and writing a conclusion. Common algebraic methods used in proofs include the distance formula, identifying parallel and perpendicular lines, and finding midpoints. Examples provided are proving properties of right triangles, trapezoids, and triangles.
Coordinate proofs
This document discusses using coordinate geometry to prove theorems about shapes in geometry. It states that it is easiest to work with shapes that are aligned with the x- and y-axes, like right triangles oriented with legs parallel to the axes or trapezoids and parallelograms aligned with the axes. It provides examples of using coordinates to prove properties about the midpoint of a hypotenuse, the median of a trapezoid, and the altitudes of a triangle. Finally, it lists five methods used in coordinate proofs, such as using the distance formula to prove line segments are equal in length.
The Properties Of A Rhombus
A rhombus is an equilateral parallelogram with four equal sides and diagonals that are perpendicular bisectors of each other. Key properties include having two sets of congruent isosceles triangles formed by its diagonals, interior and exterior angles that sum to 360 degrees, and an area calculated as half the product of its two diagonals or as base times altitude.
Obj. 7 Midpoint and Distance Formulas
The student is able to (I can):
• Find the midpoint of two given points.
• Find the coordinates of an endpoint given one endpoint
and a midpoint.
• Find the distance between two points.
Maths Quadrilateral
This document defines and provides properties of various quadrilaterals:
- A quadrilateral is a four-sided polygon with four interior angles summing to 360 degrees. Specific types include squares, rectangles, parallelograms, rhombuses, kites, trapezoids, and cyclic quadrilaterals.
- Rectangles have opposite parallel sides of equal length and right angles. Squares are rectangles with all sides of equal length.
- Parallelograms have opposite parallel sides of equal length and opposite angles summing to 180 degrees. Rhombuses are parallelograms with all sides of equal length.
- Kites have two pairs of equal sides adjacent to each other and perpendicular diagon
Coordinate geometry
The document discusses topics in coordinate geometry including slopes, length of line segments, midpoints, and proofs. It provides formulas and examples for calculating slopes, lengths of lines, and midpoints. It also discusses using an analytical approach to prove geometric theorems through using coordinates, formulas, and algebraic manipulations rather than relying solely on diagrams.
Coordinate geometry
This document provides information on various concepts in elementary and additional mathematics including:
- The distance, midpoint, and gradient formulas for lines
- Equations of lines
- Parallel and perpendicular lines
- Intersecting lines and finding intersection points
- Perpendicular bisectors
- Finding the area of polygons
It includes examples of applying these concepts to solve problems involving lines, midpoints, gradients, intersections, perpendiculars, and calculating areas.
Image compression using genetic programming
The fast growth in digital image applications such as web sites, multimedia and even personal image archives encouraged researchers to develop advanced techniques to compress images. Many compression techniques where introduced whether reversible or not. Most of those techniques were based on statistical analysis of repetition or mathematical transforming to reduce the size of the image. This research is concerning in applying Genetic programing (GP) technique in image compression. In order to achieve that goal, a parametric study was carried out to determine the optimum combination of (GP) parameters to achieve maximum quality and compression ratio. For simplicity the study considered 256 level gray scale image. A special C++ software was developed to carry out all calculations, the compressed images was rendered using Microsoft Excel. Study results was compared with JPEG results as one of the most popular lossy compression techniques. It is concluded that using optimum (GP) parameters leads to acceptable quality (objectively and subjectively) corresponding to compression ratio ranged between 2.5 and 4.5.
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...National Information Standards Organization (NISO)
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.How to Make a Field Mandatory in Odoo 17
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Build a Module in Odoo 17 Using the Scaffold Method
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaAdvanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
More Related Content
Viewers also liked
6 1 coordinate proofs
Analytic geometry uses algebraic methods to study and prove geometric problems using coordinates. This chapter discusses using coordinate proofs to prove theorems from geometry. It provides instructions on how to construct a coordinate proof by drawing and labeling a diagram, listing given information, stating what will be proved, using algebra to add to the diagram and prove the statement, and writing a conclusion. Common algebraic methods used in proofs include the distance formula, identifying parallel and perpendicular lines, and finding midpoints. Examples provided are proving properties of right triangles, trapezoids, and triangles.
Coordinate proofs
This document discusses using coordinate geometry to prove theorems about shapes in geometry. It states that it is easiest to work with shapes that are aligned with the x- and y-axes, like right triangles oriented with legs parallel to the axes or trapezoids and parallelograms aligned with the axes. It provides examples of using coordinates to prove properties about the midpoint of a hypotenuse, the median of a trapezoid, and the altitudes of a triangle. Finally, it lists five methods used in coordinate proofs, such as using the distance formula to prove line segments are equal in length.
The Properties Of A Rhombus
A rhombus is an equilateral parallelogram with four equal sides and diagonals that are perpendicular bisectors of each other. Key properties include having two sets of congruent isosceles triangles formed by its diagonals, interior and exterior angles that sum to 360 degrees, and an area calculated as half the product of its two diagonals or as base times altitude.
Obj. 7 Midpoint and Distance Formulas
The student is able to (I can):
• Find the midpoint of two given points.
• Find the coordinates of an endpoint given one endpoint
and a midpoint.
• Find the distance between two points.
Maths Quadrilateral
This document defines and provides properties of various quadrilaterals:
- A quadrilateral is a four-sided polygon with four interior angles summing to 360 degrees. Specific types include squares, rectangles, parallelograms, rhombuses, kites, trapezoids, and cyclic quadrilaterals.
- Rectangles have opposite parallel sides of equal length and right angles. Squares are rectangles with all sides of equal length.
- Parallelograms have opposite parallel sides of equal length and opposite angles summing to 180 degrees. Rhombuses are parallelograms with all sides of equal length.
- Kites have two pairs of equal sides adjacent to each other and perpendicular diagon
Coordinate geometry
The document discusses topics in coordinate geometry including slopes, length of line segments, midpoints, and proofs. It provides formulas and examples for calculating slopes, lengths of lines, and midpoints. It also discusses using an analytical approach to prove geometric theorems through using coordinates, formulas, and algebraic manipulations rather than relying solely on diagrams.
Coordinate geometry
This document provides information on various concepts in elementary and additional mathematics including:
- The distance, midpoint, and gradient formulas for lines
- Equations of lines
- Parallel and perpendicular lines
- Intersecting lines and finding intersection points
- Perpendicular bisectors
- Finding the area of polygons
It includes examples of applying these concepts to solve problems involving lines, midpoints, gradients, intersections, perpendiculars, and calculating areas.
Image compression using genetic programming
The fast growth in digital image applications such as web sites, multimedia and even personal image archives encouraged researchers to develop advanced techniques to compress images. Many compression techniques where introduced whether reversible or not. Most of those techniques were based on statistical analysis of repetition or mathematical transforming to reduce the size of the image. This research is concerning in applying Genetic programing (GP) technique in image compression. In order to achieve that goal, a parametric study was carried out to determine the optimum combination of (GP) parameters to achieve maximum quality and compression ratio. For simplicity the study considered 256 level gray scale image. A special C++ software was developed to carry out all calculations, the compressed images was rendered using Microsoft Excel. Study results was compared with JPEG results as one of the most popular lossy compression techniques. It is concluded that using optimum (GP) parameters leads to acceptable quality (objectively and subjectively) corresponding to compression ratio ranged between 2.5 and 4.5.
Viewers also liked (8)
Recently uploaded
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...National Information Standards Organization (NISO)
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.How to Make a Field Mandatory in Odoo 17
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Build a Module in Odoo 17 Using the Scaffold Method
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaAdvanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.Recently uploaded (20)
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
Slope
- 1. Finding the Slope of a line ( x, y )
- 2. The Formula O Finding the slope of a line can be difficult at first, but once you memorize the formula it is really super easy. O y–y Slope!!! x–x
- 3. Learn it! O You are given the coordinates (2,2) and (5,1) find the slope. O Find x and y for both coordinates x =2 and 5 y =2 and 1 Plug it in! 2–1 1 2 -- 5 --3