The document provides information about calculating the slope of a line from a graph or two points, including examples and practice problems. Key terms are defined, such as rise, run, slope, dependent and independent variables. An example problem demonstrates how to find the slope from a table of gas costs and gallons and interpret what the slope represents. A lesson quiz provides practice finding slopes and interpreting what they represent based on graphs and tables.
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This is a power point presentation on linear equations in two variables for class 10th. I have spent 3 hours on making this and all the equations you will see are written by me.
Linear equations in two variables- By- PragyanPragyan Poudyal
This is a power point presentation on linear equations in two variables for class 10th. I have spent 3 hours on making this and all the equations you will see are written by me.
AN EQUATION WHICH CAN BE WRITTEN IN THE FORM OF ax+by+c=0 WHERE a,b and c ARE REAL NUMBERS.
YOU WILL GET TO KNOW HOW TO REPRESENT THE EQUATIONS IN A GRAPH.
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This powerpoint presentation discusses or talks about the topic or lesson System of Equations involving Quadratic Equations. It also discusses and explains the rules, steps and examples of System of Equations involving Quadratic Equations
AN EQUATION WHICH CAN BE WRITTEN IN THE FORM OF ax+by+c=0 WHERE a,b and c ARE REAL NUMBERS.
YOU WILL GET TO KNOW HOW TO REPRESENT THE EQUATIONS IN A GRAPH.
Mathematics 9 Lesson 1-D: System of Equations Involving Quadratic EquationsJuan Miguel Palero
This powerpoint presentation discusses or talks about the topic or lesson System of Equations involving Quadratic Equations. It also discusses and explains the rules, steps and examples of System of Equations involving Quadratic Equations
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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For more information, visit-www.vavaclasses.com
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The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
1. Slope Teacher: Mr. Valdivia Email – [email_address] Grade Level: 8 Subject: Mathematics NGSSS: MA.8.A.1.2 Interpret the slope…when graphing a linear equation for a real-world problem. Also MA.8.A.1.1
2. Opening Questions Have you ever been skiing? What is the difference between a beginner’s trail, often called the bunny slope, and the expert’s trail, often called the black diamond slope? Which one of the two would have a steeper slope? Can we calculate the slope of a trail? Click for video http://player.discoveryeducation.com/index.cfm?guidAssetId=086D0622-99B1-4997-BADE-0166B07F6625&blnFromSearch=1&productcode=US
3. Rise: The vertical change when the slope of a line is expressed as the ratio rise/run. Run: The horizontal change when the slope of a line is expressed as the ratio rise/run. Slope: A measure of steepness (or constant rate of change) of a line on a graph . Vocabulary Distancia Vertical: El cambio vertical cuando la pendiente de una linea se expresa como la razon distancia vertical/distancia horizontal Distancia Horizontal: El cambio horizontal cuando la pendiente de una linea se expresa como la razon distancia vertical/distancia horizontal. Pendiente: Medida de la inclinacion (o la tasa de cambio constante) de una linea en una grafica. Razon de la distancia vertical a la distancia horizontal. Vocabulario
4. The constant rate of change of a line is called the slope of the line. The rise is the difference of the y-values of two points on a line. The run is the difference in the x-values of two points on a line. The slope of a line is the ratio of rise to run for any two points on the line. Y is the dependent variable . X is the independent variable .
5. (5, 4) (1, 2) Then count horizontally to a second point to find the run. Count vertically from any one point on the line to find the rise. Finding the Slope of a Line slope = = 2 4 1 2 The slope of the line is . 1 2 – 2 – 4 slope = = 1 2
6. (3, 2) (–1, –2) Then count horizontally to a second point to find the run. Count vertically from any one point on the line to find the rise. Finding the Slope of a Line slope = = 1 4 4 The slope of the line is 1. – 4 – 4 slope = = 1
7. If you know any two points on a line, or two solutions of a linear equation, you can find the slope of the line without graphing. The slope m of a line through the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is as follows: y 2 – y 1 x 2 – x 1 m =
8. Find the slope of the line that passes through (–2, –3) and (4, 6). Finding Slope, Given Two Points Let ( x 1 , y 1 ) be (–2, –3) and ( x 2 , y 2 ) be (4, 6). Substitute 6 for y 2 , –3 for y 1 , 4 for x 2 , and –2 for x 1 . 6 – (–3) 4 – (–2) 9 6 = The slope of the line that passes through (–2, –3) and (4, 6) is . 3 2 = y 2 – y 1 x 2 – x 1 3 2 =
9. Find the slope of the line that passes through (–4, –6) and (2, 3). Finding Slope, Given Two Points Let ( x 1 , y 1 ) be (–4, –6) and ( x 2 , y 2 ) be (2, 3). Substitute 3 for y 2 , –6 for y 1 , 2 for x 2 , and –4 for x 1 . 3 – (–6) 2 – (–4) 9 6 = The slope of the line that passes through (–4, –6) and (2, 3) is . 3 2 = y 2 – y 1 x 2 – x 1 3 2 =
10. Example Problem The table shows the total cost of gas per gallon. Use the data to make a graph. Find the slope of the line and explain what it shows. Graph the data. Cost of Gas Gallons Cost 0 0 3 6 6 12 6 9 9 12 6 0 3 3 x y Gallons Cost of Gas Cost
11. Example Problem Continued Find the slope of the line: The slope of the line is 2. This means that for every gallon of gas, you will pay another $2. = y 2 – y 1 x 2 – x 1 6 3 = 12 – 6 6 – 3 = 2
12. The slope of a line my be positive, negative, zero, or undefined.
13. The slope of a line my be positive, negative, zero, or undefined.
14. Lesson Quiz: Part I 1. (4, 3) and (–1, 1) 2. (–1, 5) and (4, 2) Assessment Find the slope of the line passing through each pair of points. 2 5 5 3
15. Lesson Quiz: Part II 3. The table shows how much money Susan earned as a house painter for one afternoon. Use the data to make a graph. Find the slope of the line and explain what it shows. Assessment x y 6 4 2 8 10 12 14 0 10 20 30 40 50 60 70 80 The slope of the line is 7. This means Susan earned $7 for each hour worked.
16. 2. The table shows the number of hours a student works and her earnings. Identify the slope of the line and explain what it shows. A. The slope of the line is 15. This means that the student earns $15 for every hour that she works. B. The slope of the line is 30. This means that the student earns $30 for every hour that she works. Quiz Student Response
![Slope Teacher: Mr. Valdivia Email – [email_address] Grade Level: 8 Subject: Mathematics NGSSS: MA.8.A.1.2 Interpret the slope…when graphing a linear equation for a real-world problem. Also MA.8.A.1.1](https://image.slidesharecdn.com/slope-111105222405-phpapp02/85/Slope-1-320.jpg)
