Algebra (NCTM) Represent and analyze mathematical situations and structures using algebraic symbols. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope. Grade 8 Curriculum Focal Points (NCTM) Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems. Connections to the Grade 8 Focal Points (NCTM) Geometry: Given a line in a coordinate plane, students understand that all 'slope triangles' - triangles created by a vertical 'rise' line segment (showing the change in y), a horizontal 'run' line segment (showing the change in x), and a segment of the line itself - are similar. They also understand the relationship of these similar triangles to the constant slope of a line. You are here: Home → Worksheets → Linear equationsFind here an unlimited supply of printable worksheets for solving linear equations, available as both PDF and html files. You can customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more. The worksheets suit pre-algebra and algebra 1 courses (grades 6-9). You can choose from SEVEN basic types of equations, ranging from simple to complex, explained below (such as one-step equations, variable on both sides, or having to use the distributive property). Customize the worksheets using the generator below. Basic instructions for the worksheetsEach worksheet is randomly generated and thus unique. The answer key is automatically generated and is placed on the second page of the file. You can generate the worksheets either in html or PDF format — both are easy to print. To get the PDF worksheet, simply push the button titled "Create PDF" or "Make PDF worksheet". To get the worksheet in html format, push the button "View in browser" or "Make html worksheet". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then edit it in Word or other word processing program. Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:
Ready-made worksheetsSee alsoWorksheets for simplifying expressions Worksheets for evaluating expressions with variables Worksheets for writing expressions with variables from verbal expressions Worksheets for linear inequalities
 Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system. => Learn more
Related Topics: • Students use a table to find solutions to a given linear equation and plot the solutions on a coordinate plane. Lesson 12 Summary• A two-variable linear equation in the form ax + by = c is said to be in standard form. b. Find five solutions to the linear equation, and plot the solutions as points on a coordinate plane.
2. Find five solutions for the linear equation 3x + y = 15, and plot the solutions as points on a coordinate plane.
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Linear equations in two variables Worksheets Grade 8 PDF
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