To properly check which statements apply to your graphed inequality, we need to consider the characteristics of the inequality's boundary line and the area that represents the solutions. Here are how you could determine which statements might apply based on common scenarios with inequalities:
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Solutions are above the boundary line: This applies if the inequality is of the form \(y > mx + b\) or \(y \geq mx + b\).
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Solutions are below the boundary line: This applies if the inequality is of the form \(y < mx + b\) or \(y \leq mx + b\).
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Solutions are on the boundary line: This applies if the inequality includes equality (for instance, \(y \leq mx + b\) or \(y \geq mx + b\)).
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There are no solutions to this linear inequality: This would only apply in a scenario where the lines defined by the inequality do not overlap or intersect in any way, which is quite rare unless the statements are contradictory.
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The boundary line has a negative slope: This applies if the slope of the line (represented as \(m\) in \(y = mx + b\)) is negative, indicating that as \(x\) increases, \(y\) decreases.
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The boundary line has a positive slope: This applies if the slope is positive, meaning that as \(x\) increases, \(y\) also increases.
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The boundary line has a zero slope: This applies if the line is horizontal, which means that \(y\) remains constant regardless of \(x\).
To answer accurately, you should visually examine your graph and determine the nature of the boundary line as well as the corresponding solution area based on the given inequality.
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