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Graphing Systems of Inequalities definitions

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  • Inequality
    A mathematical statement comparing two expressions using symbols like <, >, ≤, or ≥, indicating a range of possible solutions.
  • Solid Line
    A boundary on a graph drawn when the inequality includes equality (≤ or ≥), showing points on the line are included in the solution.
  • Dashed Line
    A boundary on a graph drawn when the inequality excludes equality (< or >), showing points on the line are not included in the solution.
  • Test Point
    A coordinate selected and substituted into an inequality to determine which side of a boundary should be shaded.
  • Shaded Region
    The area on a graph representing all points that satisfy a given inequality or system of inequalities.
  • System of Inequalities
    A set of two or more inequalities graphed on the same coordinate plane, with solutions found in overlapping shaded regions.
  • Overlapping Region
    The area where shaded regions from multiple inequalities intersect, representing solutions that satisfy all inequalities.
  • Slope-Intercept Form
    An equation format y = mx + b, making it easier to graph lines and determine shading for inequalities.
  • Parabola
    A U-shaped curve on a graph, typically representing quadratic equations, used as a boundary in nonlinear inequalities.
  • Vertex
    The turning point of a parabola, indicating the minimum or maximum value of a quadratic boundary.
  • Boundary
    A line or curve on a graph that separates regions where an inequality is true from where it is false.
  • Linear Inequality
    An inequality involving a linear equation, resulting in a straight boundary line on a graph.
  • Nonlinear Inequality
    An inequality involving a nonlinear equation, such as a quadratic, resulting in a curved boundary on a graph.
  • Solution Region
    The set of all points on a graph that satisfy every inequality in a system, often found by overlapping shaded areas.
  • Y-Intercept
    The point where a graph crosses the y-axis, often used as a starting point for graphing lines and curves.