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Understanding Commutative Properties and Linear Equations in Algebra

This guide delves into the commutative property of operations and its applications in algebra, including independent and dependent variables. Learn about different types of lines—horizontal, vertical, diagonal, and quadratic—and how to interpret function notation. Discover the meaning of slope, y-intercepts, and x-intercepts, along with methods to graph linear equations. Explore standard and slope-intercept forms in detail, emphasizing the significance of slopes in parallel and perpendicular lines. This comprehensive overview is perfect for improving your algebra skills.

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Understanding Commutative Properties and Linear Equations in Algebra

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  1. Commutative = Property Property = Commutative

  2. PROCESS Dependent Independent * Equation is Algebraic Pattern

  3. INDEPENDENT VARIABLE DEPENDENT VARIABLE

  4. Domain is reasonable data for the independent variableRange is reasonable data for the dependent variable

  5. Four Types of Lines Horizontal Diagonals Vertical

  6. Quadratic/ Parabola/ u-shaped y = x squared y= x2

  7. F(X) = y “Function Notation”Functions for every input (x) there can only be one output(y)

  8. y-intercept (0,b) X-intercept (x,0)

  9. Slope slant of the linemrise over run y over xmountainsteepness of a line Triangle means change

  10. Parallel Line Same Slope m = 3 m = 3

  11. Perpendicular LineOpposite/Reciprocal Slopes m = 2 m = - 1/2

  12. Methods for Graphing Linear Equations • Create a Table • Use x and y intercepts • Slope intercept form y=mx + b

  13. Slope Intercept Form y=mx + b y-dependent variable m-slope b-yintercept x-independent variable

  14. Standard Form Ax +By = C-A/B = slopeC is a constant

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