QQuestionMathematics
QuestionMathematics
Which is the graph of linear inequality 2y > x – 2?
# 2017
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Answer
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Step 1:I'll solve this step-by-step using the guidelines you specified:
Step 2:: Understand the Inequality
- The inequality is $$2y > x - 2
- This means we need to rearrange the equation to solve for y
Step 3:: Rearrange the Inequality
y > \frac{1}{2}x - 1
- Add 2 to both sides: - Divide both sides by 2: - Rearrange to standard form:
Step 4:: Analyze the Graph
* Slope of $$\frac{1}{2}
- This is a linear inequality - The line will have: * y-intercept of - 1 - The inequality sign (>) means the ENTIRE REGION ABOVE the line is shaded
Step 5:: Identify Characteristics
- The line passes through points (0, - 1) and (2, 0) - The shaded region is ABOVE the line - This matches graph C in the image
Final Answer
Graph C represents the solution to the inequality 2y > x - 2.
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