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Linear Inequalities in Two Variables definitions

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  • Linear Inequality
    An algebraic statement comparing two expressions using symbols like <, >, ≤, or ≥, involving two variables.
  • Ordered Pair
    A set of two numbers, typically written as (x, y), representing a point's location on a coordinate plane.
  • Solution Region
    The shaded area on a graph where all points satisfy a given linear inequality.
  • Solid Line
    A boundary on a graph indicating that points on the line are included in the solution set (for ≤ or ≥).
  • Dashed Line
    A boundary on a graph showing that points on the line are not included in the solution set (for < or >).
  • Inequality Symbol
    A sign such as <, >, ≤, or ≥ used to compare two expressions in an inequality.
  • Test Point
    A chosen coordinate, often (0,0) or another simple value, used to determine which side of the boundary to shade.
  • Slope-Intercept Form
    An equation format y = mx + b, making it easy to graph lines and identify slope and y-intercept.
  • Boundary Line
    The line on a graph that separates the solution region from the non-solution region for an inequality.
  • Standard Form
    An equation format Ax + By = C, commonly used for linear equations and inequalities.
  • Coordinate Plane
    A two-dimensional surface defined by an x-axis and y-axis, used to plot points, lines, and regions.
  • Y-Intercept
    The point where a line crosses the y-axis, indicating the value of y when x is zero.
  • Shaded Region
    The area on a graph representing all solutions to a linear inequality.
  • Greater Than or Equal To
    A comparison indicating values that are either larger than or exactly equal to another value (symbol: ≥).
  • Less Than or Equal To
    A comparison indicating values that are either smaller than or exactly equal to another value (symbol: ≤).