This equation has three variables, so it represents the three-dimensional equivalent of a line: a plane. To make the graph, we'll need to make three interceptions, er, find three intercepts. Sorry, we've got football on the brain.
Linear equations in two dimensions are represented on a graph as lines. Guess what linear equations with three variables look like on a graph? They look like planes—and not the kind with pilots.
contains JAVA applets for exploring linear and quadratic functions. Linear explorations include representations of linear functions, functions defined on intervals, equivalent expressions for functions, addition/subtraction, transformations, rate of change. Quadratic explorations equivalent quadratic expressions, comparisons and operations, solving equations, graph transformations (vertex form), add functions (polynomial form), products of linear functions, quadratic growth, graphic design, motion at changing speed, and economic decisions.
by the Concord Consortium has eight free secondary math interactives written in Java to assist algebra learners in the study of functions. "Each interactive provides a real-time connection between representations of the mathematics (symbolic, graphical, etc.), so that changes in one representation instantly cause changes in the other." Interactives include a qualitative grapher, piecewise linear grapher, linear transformer, quadratic transformer, function analyzer, system solver, plop it and proportioner. A user's guide, warm up exercise, frequently asked questions, and sample activity are provided. Also see.
from the Math Forum contains a number of interactive tools for understanding concepts related to K-12 mathematics and calculus. Help kindergarten students understand concepts. Introduce topics with pattern blocks, number lines, fraction bars and more. Algebra concepts include number systems, integers and integer operations, properties (commutative, associative, distributive), multiplying/dividing, using variables, equivalent equations, inverse operations, graphing, linear equations and systems, quadratic equations, factoring, and more. Geometry interactives for plane and solid topics are extensive. Trigonometry includes the Law of Sines and Law of Cosines. There is a range of calculus tools for differentiation and integration topics. Math Tools also contains resources (e.g., tools, activities, lesson plans, and other support materials) for such as iPad, Android phones, iPhones, and so on.
Success on the SAT comes with sound strategy, confidence, and focused practice. In the first session of your class, you'll learn the Kaplan Method for Math and the Kaplan Method for Reading Comprehension, refined strategic tools that will boost your confidence and enable you to complete practice questions and passages more effectively.You'll learn to apply the Kaplan Method for Reading Comprehension to identify passage types, create passages maps, and confidently predict and match correct answers in Reading.The Kaplan Method for Math will help you through both the Calculator and No Calculator Math tests. Your first step is applying it to linear equations in algebra.
This two-day lesson is visually based using Powerpoint presentation, Smartboard notebook presentation, and GeoGebra with interactive kinesthetic exercises. So students will follow teacher with classroom examples- using handout of graph paper. After graphing examples in class, students will haveclassroom assignment using GeoGebra- exploring solutions of 2 linear equations manipulating slope (m) and y intercept (b) of each equation.
An interesting way to expose eighth grade students to solving systems of equations by the method of substitution is to have them complete practice problems by hand and using technology. Solving systems both ways can help students view technology as an excellent math resource and increase their appreciation for using technology for academic purposes. For this three-day lesson, students are introduced to the method, solve sample problems by hand, and then use graphing calculators (such as a Texas Instrument-83 or 84) to graph the systems. Afterwards, students complete a scavenger hunt of solving systems by substititution. Using the graphing calculator in this lesson will help student understand that the solution of a system of linear equations is the intersection point of the two linear functions. It also emphasizes that solving the system of equations using an algorithm such as substitution will yield the same answer as solving the system of equations by graphing. This particular concept was difficult for my current eighth grade students to understand, but using the graphing calculators in the manner described can potentially help bridge that gap.
In this lesson, students will learn to graph, analyze, and solve systems of equations by using slope- intercept, standard, and point- slope forms of equations. Students will learn how to find 1 solution, no unique solution, or no solution by graphing system of equations. Emphasis will be on graphing systems of equations, with students leveraging their graphing skills as well as using GeoGebra to capture exact solutions. The primary math involved in solving systems by graphing is graphing. By graphing these linear equations, the solution needs to be common to both equations. By graphing these linear equations, students in addition will have to perform substitution to verify the solution is valid for both equations.
4. Model with mathematics. In grade 8, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students solve systems of linear equations and compare properties of functions provided in different forms. Students use scatter plots to represent data and describe associations between variables. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context.
The Kaplan Method for Math will help you through both the Calculator and No Calculator Math tests. Your first step is applying it to linear equations in algebra.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.