Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They use symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). Understanding how to interpret and manipulate inequalities is essential for graphing them accurately.
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Graphing Linear Equations
Graphing linear equations involves plotting points on a coordinate plane that satisfy the equation. The equation can often be expressed in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. For inequalities, the graph will include a boundary line and shading to indicate the solution set.
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Categorizing Linear Equations
Boundary Lines
In the context of inequalities, boundary lines are the lines that represent the equality part of the inequality. For example, in the inequality x < 3 + 2y, the boundary line is derived from the equation x = 3 + 2y. Depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥), the line will be dashed or solid, respectively, indicating whether points on the line are included in the solution set.
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