Algebra I Chapter 5 Study Guide Writing Linear Equations Name ________________ Due: Tuesday‚ January 17 (Exam week) 100 points Writing Linear Equations in a Variety of Forms Using given information about a __________‚ you can write an ________________of the line in _____________ different forms. Complete the chart: Form (Name) Equation • • Important information The slope of the line is ____. The __ - ___________ of the line is _____. The slope of the line is _____. The line
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2014/9/16 Linear Equations Ad Options Ads by Vidx Linear Equations A linear equation is an equation for a straight line These are all linear equations: y = 2x+1 5x = 6+3y y/2 = 3 x Let us look more closely at one example: Example: y = 2x+1 is a linear equation: The graph of y = 2x+1 is a straight line When x increases‚ y increases twice as fast‚ hence 2x When x is 0‚ y is already 1. Hence +1 is also needed So: y = 2x + 1 Here are some example values: http://www.mathsisfun.com/algebra/linear-equations
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Application of linear algebraic equation for chemical engineering problem The chemical engineering system models often outcome of set of linear algebraic equations. These problems may range in complexity from a set of two simultaneous linear algebraic equations to a set involving 1000 or even 10‚000 equations. The solution of a set two or three linear algebraic equations can be obtained easily by the algebraic elimination of variables or by the application of cramer’s rule. However for systems involving
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Applications: Graphing Simultaneous Equations − − − − Relating linear graphs and simultaneous equations Analysing graphs Practical applications of linear graphs Writing algebraic equations Jane Stratton Objectives: • Use linear graphs to solve simultaneous equations • Use graphs of linear equations to solve a range of problems • Translate worded problems into graphical and algebraic form Finding the Solution to an Equation from a graph • Finding solutions to an equation when we have a graph is easy
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LINEAR ALGEBRA Paul Dawkins Linear Algebra Table of Contents Preface............................................................................................................................................. ii Outline............................................................................................................................................ iii Systems of Equations and Matrices.............................................................................................
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direction of the jetstream. The return trip against the jetstream took four hours. What was the jet’s speed in still air and the jetstream’s speed? 3 ) These circles are identical. What is the value of x ? 4 ) Solve for x using these two equations: 2x + 6 = y; y - x = 2 5 ) The perimeter and the area of this shape are equal. What is the value of x? 6) Shobo’s mother’s present age is six times Shobo’s present age . Shobo’s age five years from now will be one third of his mother’s present
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Initialise Clear the workspace and load Linear Algebra package > restart; > with(LinearAlgebra): If you want practice at hand calculation you should use the worksheet "Interactive Gaussian Elimination" (see Menu) Enter the matrix of coefficients and right-hand side vector You may edit the following statements or use the matrix and vector pallettes to enter new data ( see View‚ Palettes) > A:=<<4 | 2 | 3 | 2> ‚ <8 | 3 | -4 | 7> ‚ <4 | -6 | 2 | -5>>; > b:=<<15‚ 7‚ 6>>;
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Linear Regression & Best Line Analysis Linear regression is used to make predictions about a single value. Linear regression involves discovering the equation for a line that most nearly fits the given data. That linear equation is then used to predict values for the data. A popular method of using the Linear Regression is to construct Linear Regression Channel lines. Developed by Gilbert Raff‚ the channel is constructed by plotting two parallel‚ middle lines above and below a Linear Regression
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Balancing Equations Balancing equations is a fundamental skill in Chemistry. Solving a system of linear equations is a fundamental skill in Algebra. Remarkably‚ these two field specialties are intrinsically and inherently linked. 2 + O2 ----> H2OA. This is not a difficult task and can easily be accomplished using some basic problem solving skills. In fact‚ what follows is a chemistry text’s explanation of the situation: Taken from: Chemistry Wilberham‚ Staley‚ Simpson‚ Matta Addison Wesley
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Linear programming is a technique which shows practical problems as a series of mathematical equations which can be manipulated to find the optimum or best solution. Blending is a graphical approach to linear programming which deals with resource allocation subject to constraints. It is a model which assists firms in deciding the best possible utilisation of limited resources. Each resource constraint is represented as a mathematical linear equation. A linear expression is an equation which links
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