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).
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
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.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Home assignment II on Spectroscopy 2024 Answers.pdf
Alg. 1 day 60 6 4 point slope form
1. DO NOW 1. From your notes or your memory, write the formula for the slope of a line when you have 2 points. 2. Write down 2 methods we have used to graph a line. 3. y = mx + b. If y = 3x + 1, what is m? What is b? 4. Ax + By = C. If 3x - 4y = 7, what is B? A? C? 5. y - y 1 = m(x - x 1 ). If y - 6 = 3(x - 2), what is x 1 ? y 1 ? m?
2. Agenda Monday, Dec. 6 Do No Homework Check homework 16 p. 307 # 2 - 18 evens Point Slope form 6-4 Ex. 1 & 2
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6. Point-Slope Form of Linear Equations Suppose you know that a line passes through the point (3,4) with a slope of 2. You can quickly write an equation of the line using point-slope form. ( y - y 1 ) = m ( x - x 1 ) ( x 1 , y 1 ) is a point on the line and m is the slope. So the difference in y equals the slope times the difference in x. m = ( y - y 1 ) ( x - x 1 )
7. POINT-SLOPE FORM m = y 2 - y 1 x 2 - x 1 y - 5 = ¾ (x - 1 ) Point = (1, 5) Slope = ¾ y - y 1 = m (x - x 1 ) (x 2 - x 1 ) (x 2 - x 1 ) m = y 2 - y 1 x 2 - x 1
8. Graphing Using Point-Slope form Graph the equation ( y - 1) = 2/3( x - 3). The equation shows that the line passes through the point (3, 1) with a slope of 2/3. Start at (3, 1), go up 2 units and right 3 units. Draw your line.
9. Now you try Graph the equation y - 4 = 2( x - 3) Start at (3, 4) go up 2 and right 1.
10. From each equation, name the slope and a point on the line. y - 4 = 3/2 (x - 1 ) 3/2 (1, 4) y - 2 = 3 (x - 5 ) 3 (5, 2) y - 6 = x - 6 1 (6, 6) y + 2 = -3(x + 4) -3 (-4, -2) y - 1 = 1/2(x + 1/2) 1/2 (-1/2, 1) y + 6 = x 1 (0, -6) y - y 1 = m (x - x 1 ) m m m m m m (x 1 , y 1 ) (x 1 , y 1 ) (x 1 , y 1 ) (x 1 , y 1 ) (x 1 , y 1 ) (x 1 , y 1 )
11. Write an equation in point-slope form of the line that passes through the point (2, 5) and has a slope of 3. ( y - y 1 ) = m ( x - x 1 ) Substitute the 5 in for y 1 , the 2 in for x 1 and the 3 in for m. y - 5 = 3 ( x - 2 )
12. Now you try: Write the equation of the line with a slope of -3 that passes through the point (-1, 7) in point-slope form. ( y - 7) = -3( x + 1) Write the equation of the line with a slope of 2/3 that passes through the point (10, -8). y + 8 = 2/5(x - 10)
13. Write an equation in point-slope form which goes through the given point(s) with the information given. m = 2 m = -3/2 m = 1/4 m = 1 pt. = (3, 5) pt. = (4, 3) pt. = (-4, -2) pt. = (9, -1) y - 5 = 2(x - 3) y - 3 = -3/2(x - 4) y + 2 = 1/4(x + 4) y + 1 = x - 9 y - y 1 = m (x - x 1 ) y - y 1 = m (x - x 1 ) y - y 1 = m (x - x 1 ) y - y 1 = m (x - x 1 ) y - y 1 = m (x - x 1 )
16. Point Slope Form - Things to Remember COPY · It's just a linear equation in a different format. · · When given slope and a point, plug them both in. · · Watch out for negatives. · · When given 2 points, find slope, then use that slope and either point. · · Once you use point-slope, you can change to other forms. y - y 1 = m (x - x 1 )
