Which inequality is best represented by the graph of a linear inequality on the coordinate plane?
Understand the Problem
The question is asking which linear inequality corresponds to a given graph plotted on a coordinate plane. To solve this, we would need to analyze the graph's characteristics, such as the slope and y-intercept, to match it with one of the given options.
Answer
The inequality depends on the graph characteristics, but will generally be in the form $y < mx + b$, $y \leq mx + b$, $y > mx + b$, or $y \geq mx + b$.
Answer for screen readers
The final answer will depend on the specific slope, y-intercept, and shading of the graph presented. Based on the characteristics identified above, the inequality can be expressed as $y < mx + b$, $y \leq mx + b$, $y > mx + b$, or $y \geq mx + b$.
Steps to Solve
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Identify the Slope and Y-Intercept Examine the graph to determine the slope (m) of the line and the y-intercept (b). The slope can be calculated as the rise over the run between two points on the line.
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Determine the Type of Inequality Observe whether the line is solid or dashed. A solid line indicates a "greater than or equal to" ($\geq$) or "less than or equal to" ($\leq$) inequality, whereas a dashed line indicates a "greater than" ($>$) or "less than" ($<$) inequality.
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Write the Inequality Use the slope and y-intercept to write the linear inequality in the form $y < mx + b$ or $y \leq mx + b$. Substitute in the values of m and b from the previous steps.
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Consider the Region of Solutions Shade the appropriate region of the graph. The shaded area shows where the solution to the inequality lies. Ensure the direction of shading is consistent with the inequality sign.
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Finalize the Inequality Check the direction of the inequality sign based on where the shaded area is located in respect to the line you found.
The final answer will depend on the specific slope, y-intercept, and shading of the graph presented. Based on the characteristics identified above, the inequality can be expressed as $y < mx + b$, $y \leq mx + b$, $y > mx + b$, or $y \geq mx + b$.
More Information
Choosing the correct inequality requires careful observation of the line's characteristics on the graph. Make sure to double-check the slope, the y-intercept, and whether the shading is above or below the line, as these aspects will determine the accuracy of the inequality representation.
Tips
- Misreading the slope or intercept: Verify the points carefully.
- Confusing solid and dashed lines: Remember that solid lines mean "equal to" and dashed lines mean "not equal to."
- Incorrectly interpreting the shading: Ensure the inequality accurately reflects the shaded area; above the line corresponds to "greater than," and below corresponds to "less than."
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