PPT-Linear Equations

SlopeIntercept Form PointSlope Form Horizontal amp Vertical Lines Learning Objectives Determine the equation of a line given the slope and y intercept Determine the equation of a line given the slope and any point. e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations 3.1 – . Systems of Linear Equations in Two Variables. 1. Suppose we have two linear equations. :. . . Together, they make a ________________________________ (also called a . ___________________).. (what is that?). What . is linear algebra? Functions and equations that arise in the "real world" often involve many tens or hundreds or thousands of variables, and one can only deal with such things by being much more organized than one typically is when treating equations and functions of a single variable. Linear algebra is essentially a ". By:. Emily Zhou. What is a Linear Equation?. A linear equation is an equation whose graph forms a straight line.. Linear equations are usually shown on a coordinate plane. Real life situations of linear equations include the stock market as well as the payments of a car.. David Plaxco. Linear Independence of Functions. Definition of linear independence of vector-valued functions. :. Let . f. i. : . I . = (. a,b. ) . → . . . n. , . I = 1, 2. ,…. , n. .. . The . Introduction. This chapter gives you several methods which can be used to solve complicated equations to given levels of accuracy. These are similar to methods which computers and calculators will use, and hence can be used in computer programming. Point-Slope Form.  . The . point-slope form. allows you to use ANY point, together with the slope, to form the equation of the line.. Find the equation of a line that passes through the point . and has a slope of 3.. 1. 2. Elementary Row Operations. There are three kinds of Elementary Row Operations.. 1) Interchanging two rows.. Multiplying a row by a non-zero constant.. Adding a multiple of one row to another row.. Algebra 1: Unit 7. Graphing linear equations. Graphing Linear Equations. The steps to graphing a linear equation:. Step . 1: Create an x/y chart. Step 2: Pick two points for x. Step 3: Determine the value of y given x. Examples:. . 1). . . x 3 = 15. . 2) p – 5 = 20. 3) 2d = 16. 4). . = 24.  . Multi-Step Equations. Examples—. 5). 2p 15 = 29. 6). 14 – 3n = -10. 7). 27 = -9(y 5). 8). 7a – 3a 2a – a = 16.  .  . Solutions are found at the intersection of the equations in the system.. Types of Solutions. Section 8.1 – Systems of Linear Equations. Consistent System. One solution. Consistent System. Infinite solutions. Clayton County Summer Math Academy. Algebra I – Solving Equations & Systems. Sarah Ledford. June 9, 2015. 1. Solve it!. 2. Solve the following equation for . t. :. 105 = 100(1 + .05. t. ). Explain how you solved it & how you know your solution is correct. . New York State Next Generation Mathematics Learning StandardsGrade 8CrosswalkExpressions and Equations InequalitiesClusterNYS P-12 CCLSNYS Next Generation Learning StandardWork with radicals and integ (from 2.2 Solving linear equations). KS3 Mastery PD Materials: Exemplified Key Ideas. Materials for use in the classroom or to support professional development discussions. Summer 2021. About this resource.