January 16, 2014
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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.
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This document provides an overview of slope, parallel lines, and perpendicular lines. It defines key concepts such as slope, slope-intercept form, standard form, and point-slope form. It also discusses how to calculate slope and classify lines based on their slopes. The document notes that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. It provides examples of finding equations of parallel and perpendicular lines.
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Parallel lines have the same slope and never intersect. Two lines are parallel if their slopes are equal. The equation of a line parallel to a given line can be found using the point-slope formula with the same slope.
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Okay, let's break this down step-by-step:
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* 90% is 0.9
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* The total number of girls is 90
* So the number of girls late is 90 - 81 = 9
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* 80% is 0.8
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- It explains the slope-intercept form of a linear equation where y=mx+b, with m being the slope and b being the y-intercept.
- It gives examples of writing equations in slope-intercept form and graphing lines from their equations.
- It discusses other forms like point-slope form and how to write equations of lines given characteristics like a point and slope.
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This document discusses slope, y-intercept, and how to find and graph linear equations. It defines slope as the ratio that describes a line's tilt and explains how to calculate slope using rise over run between two points on a line. It also discusses how to find the y-intercept, and then use slope and y-intercept to write the equation of a line in y=mx+b form. Examples are provided for finding slope from tables of values and graphing linear equations on a coordinate plane.
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March 18
Okay, let's break this down step-by-step:
* 90% of 90 girls showed up on time
* 90% is 0.9
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* The total number of girls is 90
* So the number of girls late is 90 - 81 = 9
* 80% of 110 boys showed up on time
* 80% is 0.8
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* So the number of boys late is 110 - 88 = 22
* The total number of children late is the girls (9) + the boys (22)
* So the total number
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This document contains formulas and examples for key algebraic concepts like like terms, coefficients, perimeter of rectangles and triangles, and area of rectangles and triangles. It also provides warm-up problems involving translating sentences to algebraic expressions and equations, and simplifying expressions. Finally, it outlines the topics and key concepts that will be covered on Test #1: simplifying expressions by combining like terms, solving one- and two-step equations, and translating sentences into algebraic representations.
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1) It reviews formulas for the standard form, slope-intercept form, and point-slope form of linear equations. Examples are given of writing equations from points and slopes using the point-slope form.
2) Classwork problems are assigned from section 2.11 and formulas/examples are provided to help with coordinate plane test preparation on writing linear equations from graphs.
3) Additional resources like Khan Academy and online guides are mentioned for further practice with coordinate plane and linear equation concepts.
January 15
The document provides a study guide for a Power Point test covering topics from Thursday's test as well as formulas. It includes warm-up problems on ratios, unit conversions, and simplifying expressions. It reviews finding slopes and determining if lines are parallel. It discusses writing equations of lines given a point and the equation of a parallel or perpendicular line. Sample problems are worked through demonstrating how to find the equation of a line passing through a point that is parallel or perpendicular to another given line.
Module 5 topic 2
1) If line 1 has a slope of 3, the slope of a perpendicular line 2 needs to be -1/3.
2) If a line has the equation x + 4y = 7, a parallel line will have a slope of -1/4.
3) If a line has the equation x + 4y = 7, a perpendicular line will have a slope of 4.
5.5 writing linear equations
1) Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals of each other.
2) To determine if two lines are parallel or perpendicular, you calculate their slopes. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals, the lines are perpendicular.
3) To find the equation of a line parallel or perpendicular to a given line, you use the slope of the given line and the point-slope formula. For a parallel line, you use the same slope. For a perpendicular line, you use the negative reciprocal slope.
January 21, 2015
1. The document provides information on linear functions and how to determine if an equation represents a linear function. It discusses using standard form (Ax + By = C) to identify linear equations and determine intercepts.
2. The document contains examples of writing equations of lines given points and slopes in various forms. It discusses using point-slope form and converting between slope-intercept and standard form.
3. The document provides practice problems determining if graphs are functions, whether equations represent lines, finding rates of change, intercepts, and writing equations in different forms. It aims to help students work with linear functions and equations.
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.
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.
Writing Equations of a Line
1) The document discusses various forms of equations for lines, including slope-intercept form, standard form, and point-slope form. It provides definitions and examples of writing equations of lines given the slope and y-intercept or given two points on the line.
2) Key concepts covered include writing the equation of a line given its slope m and y-intercept b using slope-intercept form y=mx+b, or given slope m and a point (x1,y1) using point-slope form y-y1=m(x-x1).
3) Examples are provided for writing equations of lines using slope-intercept form when given slope and y-intercept, and using point-
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
Linear equations rev
This document discusses key concepts related to linear equations in two variables including:
1. Linear equations can be written in the form ax + by = c and are graphed as lines.
2. The slope of a line measures its steepness and is calculated using the slope formula.
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.
Dec.18
The document provides instructions for a double agent located at coordinates (-2,-3) who needs to escape to one of two safe houses. The safe houses are located in the direction of a -2/3 slope from the agent's current location. The document requests the coordinates of the two safe houses to help the agent narrowly escape death.
Maths
This document discusses linear equations in two variables. It defines linear equations in two variables as equations of the form ax + by = c, where a, b, and c are real numbers and a and b are not both zero. It explains that the graph of any linear equation in two variables is a straight line. It also categorizes different types of systems of linear equations based on the relationship between the lines: intersecting lines have a unique solution; coincident lines have an infinite number of solutions; and parallel lines have no solution. Methods for solving systems of linear equations like substitution, elimination, and graphing are also covered.
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5.5 parallel and perpendicular lines (equations) day 1
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August 23, 2016
The document provides classwork and practice problems related to algebraic expressions and one-step equations. New vocabulary terms introduced are coefficient and like terms. Examples are given of adding and subtracting like terms. There are also practice problems for translating expressions, solving one-step equations, and word problems involving algebraic relationships between variables.
August 22, 2016
This document provides instructions and examples for students on organizing their math notebooks. It includes examples of how to categorize different math concepts like properties, formulas, and vocabulary in the resource section. It also provides warm-up problems covering large and small numbers. Students are instructed to complete homework assignment 1.1 by the due date of August 23, 2016. They are also given examples of translating expressions and equations.
August 19, 2016
This document contains a math lesson on large and small numbers, number relationships, and problem solving. It includes warm-up questions about numbers greater than or less than a trillion, billions, and millions. It also has questions about the width of a human hair, distance from Earth to the Sun, and how fast a hummingbird flaps its wings. The document provides answers to the warm-up questions and has an end of week review on number operations and translating word problems into algebraic equations. It concludes with an example of solving a multi-step word problem algebraically to find the individual weights of Mike, Bob, and Don.
August 18, 2016
This document contains reminders for school supplies needed by Monday, an overview of the 5 essential understandings of algebra, and 5 fraction practice questions. The 5 essential understandings are: 1) Algebra is a method for solving math problems, not the problems themselves. 2) Mathematics uses symbols as shortcuts. 3) Algebra rules come from natural number rules. 4) Algebra examines patterns and relationships between numbers. 5) Look for equality and use it to your advantage when solving problems. Mastering multiplication tables is also emphasized.
Aug 17, 2016
The document outlines the daily routine and learning process for a math class. It includes:
1. A warm-up with 4-5 review or new problems to introduce topics for the day. Class work is to be completed during class time and any unfinished work should be done outside of class.
2. New concepts are introduced through demonstration by the teacher, then practiced together through examples before students work independently.
3. Additional learning resources like online math sites are provided to support studying outside of class, since class time is limited to 60 minutes per day.
4. A short practice test is included covering translating expressions, order of operations, and fractions to gauge readiness.
Ultimate guide to systems of equations
i) The document discusses various methods for solving systems of linear equations, including graphing, substitution, elimination, and cross-multiplication.
ii) It also addresses solving systems that can be reduced to linear equations, such as transforming non-linear equations using substitution.
iii) Examples are provided to illustrate each method for deriving the solution of a system of equations.
March 29, 2016
The document provides examples for solving systems of equations through various methods like elimination, substitution, and word problems. It demonstrates setting up systems as equations based on information provided, choosing an elimination method by adding or multiplying equations, isolating variables, substituting values, and checking solutions. Word problems are converted to systems of equations and then solved to find unknown variable values.
March 28, 2016
The document provides information about assignments and tests for today and upcoming dates. It includes notes about 4th quarter grade trackers, make-up tests during lunch, systems of equations lessons for some periods today and tomorrow, and distributing worksheets. The document also contains math content on solving systems of equations by graphing, substitution, and elimination.
March 31, 2016
The document discusses reviewing Khan Academy topics on systems of equations and solving 3x3 systems. It includes examples of solving systems of equations by elimination, addition, and substitution. Students will review methods, complete assignments, and take a five question quiz on solving systems of equations.
March 30, 2016
The document provides instructions for practicing Khan Academy topics on systems of equations word problems. It also reminds the student to make progress on homework 4.1-4.2 which is due on Friday for full credit. Examples are given for solving systems of equations by substitution and word problems involving jeans/shirts and movie tickets.
March 21, 2016
This document provides information about upcoming tests, review material, and math concepts to be covered in class. It includes:
- Details on making up remaining tests and reviewing for the final exam
- The 5 most missed questions from the last test
- Vocabulary and terms related to systems of equations to be covered
- Sample word problems and equations involving ratios, rates, percents, and lines to work on for the next class
April 5, 2016
The document provides examples and steps for solving systems of inequalities and linear equations. It discusses graphing a single inequality, the steps for graphing systems of inequalities, and provides an example of solving a two-variable linear system of inequalities. Sample problems include determining the number of hours until costs are the same for two plumbing companies and graphing the inequality y < 5x + 1.
April 4, 2016
This document contains a daily agenda and warm-up problems for math class including:
1) Solving systems of equations by graphing, substitution, and elimination. Example problems include solving for costs of flowers and costs of different internet providers over time.
2) Review of fractions, inequalities, and solving multi-step equations.
3) An example of solving a 3x3 system of equations by eliminating a variable and substituting values.
4) Warm-up questions ask students to write and solve systems of equations modeling real-world scenarios like costs of soccer equipment and costs of fitness clubs over time.
April 6, 2016
The document provides a review of topics related to solving systems of equations and inequalities including:
1) There are two methods for solving systems - elimination or substitution. An example problem is worked through using elimination.
2) When graphing systems of inequalities, each line must be drawn and labeled as above, below, or dashed before moving to the next line.
3) Word problems can be modeled with systems and solved, such as determining the number of chickens and pigs given the total number of legs.
April 1, 2016
This document contains examples of solving systems of equations word problems. It begins with a warm-up problem about a math test worth a total of 63 points made up of 2-point and 3-point problems. Then it provides steps for solving systems of equations, including labeling variables, writing equations, solving, and checking. Finally, it applies these steps to two word problems, one about movie tickets and one about flowers for Valentine's Day.
February 17 2015
The document provides instruction on calculating and interpreting slope. It defines slope as the ratio of rise over run between two points on a line. It gives the formula for calculating slope as the change in y over the change in x between two points. Several examples are worked out step-by-step to demonstrate calculating slope from graphs and point pairs. Key concepts covered include identifying horizontal and vertical lines that have slopes of 0 and undefined respectively.
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
February 16 2016
The document provides information about an upcoming test on coordinate planes and linear functions. It includes:
- A review of topics to be covered on the test like functions, ordered pairs, slope of a line, and standard form of a line.
- Examples of problems about domain and range, graphing lines, finding intercepts, and interpreting graphs.
- Instructions to have materials like graph paper and a calculator ready for working through sample problems.
- A reminder that attempting all problems is better than leaving them blank on the test.
February 9 2016
The document outlines an agenda for a math class that includes a warm-up on missed test questions, learning about functions and their domains and ranges, using the vertical line test to determine if a relation is a function, and interpreting graphs. It provides examples of mapping relations to check if they are functions and using the vertical line test. Students are given practice problems to determine if relations are functions and to graph relations and use the vertical line test.
February 10 2016
This document provides instruction on determining the domain and range of functions, identifying functions using mapping and the vertical line test, and interpreting graphs. It includes examples of determining domain and range for various functions defined by equations. Warm-up questions are provided to have students plot points and draw lines from equations. Students are reminded that their class work CW 3.4 is due for full credit.
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January 16, 2014
- 1. 16
- 2. Warm-Up: 3. Write the equation in standard form using integer coefficients only: 3y = -2/5x + 4
- 3. Warm-Up: 5. What is the equation of the line shown? y x
- 4. Practice Problems: 1. Is the graph a function? Why or why not? 2. Is the graph a linear function? Why or why not? 3. What is the per week rate of change between weeks 1-3? 4. What is the per week rate of change between weeks 6-10?
- 6. Parallel & Perpendicular Lines: Formulas & Vocabulary Section of Notebook, Please Two lines are considered parallel if they have the same slope. Two lines are considered to be perpendicular to each other if their slopes are the opposite inverse (negative reciprocal) of each other. Perpendicular lines cross each other at a 90° angle. The slope of a perpendicular line is:
- 7. Parallel & Perpendicular Lines: Let's find the equation of a line parallel to y = - x that passes through the point (2, 4) What is the slope of the first line, y = - x ? -1 y = - x (+ 0) This is in slope intercept form so y = mx + b which means the slope is –1. Use the point-slope formula to find the equation of the 2nd line y -y1= -(x - x1) y -4 = -(x - 2) y = -x + 6
- 8. Practice Problem: Write an equation of the line that passes through (–3, –5) and is parallel to the line y = 3x – 1. SOLUTION STEP 1 Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (–3, –5) has a slope of 3. STEP 2 Find the y-intercept. Use the given point and the slope.
- 9. Practice Problem: y = mx + b –5 = 3(–3) + b 4=b Write slope-intercept form. Substitute 3 for m, 3 for x, and 5 for y. Solve for b. STEP 3 Write an equation. Use y = mx + b. y = 3x + 4 Substitute 3 for m and 4 for b.
- 10. Parallel & Perpendicular Lines: Let's find the equation of a line perpendicular to y = - x that passes thru the point (2, 4) The slope of the first line is still –1. The slope of a line perpendicular is the negative reciporical so take –1 and "flip" it over and make it negative. The slope of a perpendicular line is 1 and it passes through (2, 4). Use the point-slope formula to find the equation of the 2nd line.