Questions and Answers
Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply.
Which is the graph of the linear inequality 2x - 3y < 12?
Which linear inequality is represented by the graph?
The solutions to the inequality y > -3x + 2 are shaded on the graph. Which point is a solution?
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Which is the graph of the linear inequality y ≥ -x - 3?
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Which linear inequality is represented by the graph?
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Which linear inequality is represented by the graph?
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Which is the graph of the linear inequality rac{1}{2} x - 2y > -6?
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Which linear inequality is represented by the graph?
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Study Notes
Graphing Two-Variable Linear Inequalities
- Understanding of linear inequalities can be enhanced through graphical representation, showing which areas of the graph contain solutions.
Inequality Representations
- The graph of a linear inequality can represent different forms based on its slope and intercepts.
- Example: For the inequality y < 2/3 x + 3, the area below the line is shaded.
Solution Points
- Not all points will satisfy an inequality; specific points can be checked against the inequality to confirm if they are solutions.
- Example: For y < 0.5x + 2, valid solution points include (-3, -2), (-1, -2), (1, -2), and (1, 2).
Graphing Techniques
- Graphs may indicate whether the inequality is strict (open circles) or inclusive (closed circles), guiding whether the boundary line is part of the solution set.
Inequality Form Examples
- y > −3x + 2 suggests shading above the line; points satisfying this include (2, 0).
- Inequalities such as 2x - 3y < 12 require correct graphing to determine feasible solutions visually.
Interpretation of Graphs
- Each graph representation varies with the slope-intercept format, where the coefficient of x directly influences the line's steepness.
- Identifying the correct inequality form is crucial when corresponding to a graph’s linearity.
Key Points to Remember
- When determining solutions, checking multiple points against the inequality is essential for accuracy.
- Recognize that shading indicates the area where all potential solutions to the inequality reside in relation to the boundary line.
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Description
Test your knowledge of graphing linear inequalities with this flashcard quiz. Determine which inequalities correspond to given graphs and identify solution points accurately. Perfect for visual learners and mathematics students!
