Math Problem Statement
Solution
To determine which inequality corresponds to the shaded region in the graph, let's analyze the line and shading shown in the coordinate plane.
Step 1: Identify the Line Equation
From the graph, the line appears to have:
- A y-intercept at (point ).
- A slope that goes downwards by 2 units for every 1 unit it moves right, giving a slope of .
This means the line equation is:
Step 2: Determine the Inequality
- The shading is on the region below the line, which suggests a “less than” inequality.
- Therefore, the inequality describing this shaded area would be:
Step 3: Match with the Options
Looking at the provided options:
- Option A: (matches our inequality, but it should be strict inequality without “equal to”)
- Option C: (incorrect slope sign)
- Option D: (incorrect slope and inequality direction)
Answer:
The correct answer that fits the graph’s shaded region and line is:
Would you like further details or have any questions?
Here are some related questions that expand on this concept:
- How would the inequality change if the shaded region were above the line?
- How does changing the slope affect the inequality?
- What does a dashed line mean in an inequality graph?
- How do you determine the correct inequality sign based on shading?
- What role does the y-intercept play in graphing linear inequalities?
Tip: Always check if the line is solid or dashed; a solid line includes points on the line (≤ or ≥), while a dashed line excludes them (< or >).
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Math Problem Analysis
Mathematical Concepts
Algebra
Graphing Linear Inequalities
Formulas
Slope-intercept form y = mx + b
Theorems
Linear inequality graphing
Suitable Grade Level
Grades 8-10
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