Graphing Systems of Inequalities definitions Flashcards
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.
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