Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities express a relationship where one quantity is not equal to another, often using symbols like <, >, ≤, or ≥. In this case, the inequality (x−2)²+(y+1)²<9 indicates that we are looking for all points (x, y) that satisfy this condition, which defines a region rather than a specific value.
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Graphing Circles
The given inequality represents a circle centered at the point (2, -1) with a radius of 3, since the expression (x−2)²+(y+1)²=9 describes a circle. When graphing, the area inside the circle is included because of the '<' symbol, indicating that points within this radius are part of the solution set.
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Coordinate Plane
The coordinate plane is a two-dimensional surface defined by an x-axis (horizontal) and a y-axis (vertical). Understanding how to plot points and shapes on this plane is essential for graphing inequalities, as it allows for visual representation of the solution set, helping to identify which regions satisfy the given inequality.
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Graphs & the Rectangular Coordinate System