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Linear Inequalities in Two Variables definitions

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  • Linear Inequality
    A mathematical statement involving two variables and an inequality symbol, representing a region on a graph.
  • Ordered Pair
    A set of two numbers representing coordinates on a graph, used to test solutions for inequalities.
  • Solution Region
    The area on a graph where all points satisfy a given linear inequality.
  • Solid Line
    A boundary on a graph drawn when the inequality includes equality, indicating points on the line are solutions.
  • Dashed Line
    A boundary on a graph drawn when the inequality excludes equality, indicating points on the line are not solutions.
  • Slope-Intercept Form
    A way to write a linear equation or inequality as y equals mx plus b, simplifying graphing and shading.
  • Inequality Symbol
    A sign such as <, >, ≤, or ≥ used to compare expressions and determine the solution region.
  • Y-Intercept
    The point where a line crosses the y-axis, useful for graphing linear inequalities.
  • Test Point
    A chosen coordinate used to check which side of a boundary satisfies the inequality.
  • Shaded Region
    The portion of a graph representing all solutions to a linear inequality.
  • Standard Form
    A linear equation or inequality written as ax plus by equals c or ax plus by compared to c.
  • Boundary Line
    The line separating solution and non-solution regions for a linear inequality.
  • X-Axis
    The horizontal axis on a graph, often used for selecting test points.
  • Y-Axis
    The vertical axis on a graph, often used for selecting test points.
  • Slope
    A measure of the steepness of a line, crucial for graphing linear inequalities.