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This document discusses parallel and perpendicular lines in the coordinate plane. It defines slope as rise over run and provides examples of calculating slope. It states that two non-vertical lines are parallel if they have the same slope. Two non-vertical lines are perpendicular if the product of their slopes is -1. Vertical and horizontal lines are always perpendicular. The objectives are to find slopes of lines and use slopes to identify and write equations for parallel and perpendicular lines.
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Perpendicular lines intersect at a right angle. Two lines are perpendicular if the product of their slopes is -1. The equation of a line perpendicular to a given line can be found using the point-slope formula with the slope of the perpendicular line being the negative reciprocal of the given line's slope. Examples are provided of finding if lines are parallel or perpendicular and constructing parallel and perpendicular lines through a given point.
1.4.4 Parallel and Perpendicular Line Equations
Use slopes to identify parallel and perpendicular lines
Write equations of a line parallel or perpendicular to a given line through a given point.
5.5 Linear Equations Point Slope Form
The document discusses point-slope form for writing equations of lines. Point-slope form is defined as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a given point on the line. Several examples are shown of writing equations of lines in point-slope form given the slope and a point, or two points to find the slope. Converting between point-slope, slope-intercept, and standard forms is also demonstrated.
5.5 parallel perp lines
The document discusses point-slope form and writing linear equations. It provides examples of writing equations for lines that are parallel and perpendicular to given lines. Specifically, it explains that parallel lines have the same slope and different y-intercepts, while perpendicular lines have slopes that are negative reciprocals of each other. Examples are given of writing equations for parallel and perpendicular lines using point-slope form based on a given point and the slope of another line.
8.3 Slope And Y Intercept
The document discusses slope and the slope-intercept form of linear equations. It defines slope as the ratio of the rise over the run between two points on a line. Slope can be calculated using two points or using the difference of the y-coordinates over the difference of the x-coordinates. Horizontal and vertical lines have special cases for slope calculations. The slope-intercept form is defined as y=mx+b, where m is the slope and b is the y-intercept. Using this form, lines can be graphed by plotting the y-intercept and using the slope to find the second point and draw the line.
2.2 slope
1. The document discusses slope and rate of change, including how to calculate slope from two points on a line and how to interpret positive, negative, zero, and undefined slopes.
2. It provides examples of finding the slope of lines from graphs and points, and discusses how to identify parallel and perpendicular lines based on their slopes.
3. The key concepts are how to determine the steepness of a line from its slope, and that parallel lines have the same slope while perpendicular lines have slopes that are opposite reciprocals.
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.
1.4.4 Parallel and Perpendicular Line Equations
Use slopes to identify parallel and perpendicular lines.
Write equations of line parallel or perpendicular to a given line through a given point.
January 16, 2015
- The document outlines notes on slope and linear equations from a class. It includes definitions of slope, formulas for calculating slope between two points, and examples of finding the slope and equation of a line from graphical data or given information.
- Students will review slope formulas, work examples and practice problems, and complete class work 2.11 applying concepts of slope and linear equations. The notes provide guidance on finding slope, writing equations of lines in slope-intercept and standard form, and graphing lines on coordinate planes.
Linear Functions
Linear functions have a constant rate of change (slope) between any two points. The document provides methods for determining if a set of data represents a linear function, writing the equation of a line given various parameters like slope and intercepts, and properties of lines like parallel, perpendicular, vertical and horizontal lines. It also discusses how to find the equation of a perpendicular bisector by calculating the slope, midpoint and using the negative reciprocal slope in the point-slope form.
January 16, 2014
The document discusses finding equations of lines that are parallel or perpendicular to given lines. It provides the definitions that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. Examples are worked through using the point-slope formula to find equations of parallel and perpendicular lines passing through given points.
Module 4 topic 3 similar problems
This document provides examples of writing equations of linear functions in slope-intercept form. It demonstrates finding the slope from two points, using the slope and a point to write the equation in point-slope form, writing equations for horizontal and vertical lines, writing equations from tables of values, and solving linear equations for y.
Chapter 5 Slopes of Parallel and Perpendicular Lines
This document provides a lesson on identifying and writing equations for parallel and perpendicular lines. It includes examples of identifying parallel lines based on their having the same slope. Perpendicular lines are defined as having slopes whose product is -1. The document also demonstrates how to write equations for lines parallel or perpendicular to a given line based on their point and slope. Examples are provided to illustrate finding slopes from graphs and using them to determine if lines are parallel or perpendicular.
Lecture 07 a rate of change slope
This document discusses slope and rate of change for lines. It defines slope as the ratio of the change in y to the change in x between two points on a line. Slope can be calculated using the formula m=(y2-y1)/(x2-x1). Horizontal lines have a slope of 0, and vertical lines have an undefined slope. Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. Examples are provided for calculating slope, along with exercises asking students to calculate slopes for given point pairs and determine if lines are parallel or perpendicular.
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
identities1.2
The document discusses the concept of slope and how it is used to describe the steepness of a line. It defines slope as the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. Several forms of linear equations are presented, including point-slope form, slope-intercept form, and standard form. Relationships between parallel and perpendicular lines based on their slopes are also described. Examples are provided to demonstrate finding slopes, writing equations of lines, and determining if lines are parallel or perpendicular based on their slopes.
Solving Systems by Graphing
Systems of lines can relate in three ways: they can cross at a single point, be parallel, or be the same line. Parallel lines have no solution since they never intersect. The same line has an infinite number of solutions since all points satisfy both equations. Lines that cross at a single point have a unique solution that can be found by putting the point of intersection into both equations.
Finding Slope 2009
The document provides instruction on calculating the slope of a line. It defines slope as the steepness of a line and discusses how to calculate it using rise over run when given two points on a graph, or using the slope formula when given the coordinates of two points. It provides examples of finding the slope in various contexts and situations, including when the slope is defined elsewhere in the question or when lines are horizontal or vertical.
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Chapter 5 Slopes of Parallel and Perpendicular Lines
Chapter 5 Slopes of Parallel and Perpendicular Lines
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Chapter 2 notes new book
Here are two paragraphs answering the questions:
I plan to start a business from scratch. The main advantage is that I will have full control over decisions like location and facilities. However, the main disadvantage is that it will take more time and effort to build everything from the ground up compared to buying an existing business. I will need to focus on tasks like hiring and training employees, setting up equipment and inventory, and promoting the business to attract customers. It may also be more difficult to get financing without an established track record.
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Plumbing night 1 legal forms of business
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Security privacy health environmental
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Algebra 6 Point 10
(1) To square a binomial like (a + b)2, use the formula a2 + 2ab + b2. To square a difference like (a - b)2, use the formula a2 - 2ab + b2.
(2) The product of two binomials of the form (a + b)(a - b) is a2 - b2.
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Algebra 6 Point 8
This document provides instructions on how to multiply a polynomial by a monomial. It explains that to multiply terms like 3x(4x - 1), you distribute the monomial by multiplying it by each term in the polynomial. This results in 12x^2 - 3x. It then gives the example of multiplying (3y^2 - y + 6)(-2y^2), and provides more practice problems to solve involving multiplying polynomials by monomials. It directs the reader to page 227 of their materials to complete problems 1 through 9.
Algebra 6 Point 7
To add and subtract polynomials:
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2) Sort polynomials in descending order by exponent before adding or subtracting
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Algebra 6 Point 5
Scientific notation is a way to write very large and very small numbers compactly. It expresses numbers as a decimal between 1 and 10 multiplied by a power of 10. Converting between scientific notation and standard form involves moving the decimal point and changing the exponent accordingly. A scientific calculator can be used to perform calculations with numbers in scientific notation by using the exponential or EE key.
Algebra 6 Point 3
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Algebra 6 Point 4
This document discusses negative exponents and how to simplify expressions with negative and fractional exponents. Some key points:
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Algebra 6 Point 6
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Algebra 6 Point 2
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Geom 3point6and7
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