Math Problem Statement
Write the inequality shown on each graph (in slope-intercept form).
Solution
The problem asks to write the inequality represented by each graph in slope-intercept form. Let's analyze both graphs based on the image:
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Left Graph:
- The dashed line indicates the boundary of the inequality. Dashed lines suggest the inequality does not include the line itself (i.e., either "<" or ">").
- The line crosses the y-axis at and has a slope of . This can be verified by noting that the line moves down 2 units for every 1 unit it moves to the right.
- So, the equation of the line in slope-intercept form is .
- Since the shading is below the line, the inequality will be .
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Right Graph:
- The solid line means the inequality includes the boundary line (i.e., either "≤" or "≥").
- The line crosses the y-axis at and has a slope of , moving up 2 units for every 1 unit to the right.
- The equation of the line is .
- Since the shading is above the line, the inequality will be .
Final Inequalities:
- Left graph:
- Right graph:
Let me know if you want further explanation or have questions! Here are some related questions you might find useful:
- What is the difference between a dashed and a solid line in graphing inequalities?
- How do you find the slope of a line from a graph?
- Why does the inequality direction change based on the shading?
- Can inequalities have vertical lines, and how would you represent them?
- How would these inequalities change if the lines had different slopes?
Tip: Always check the shading and line type (solid or dashed) to correctly interpret inequalities on a graph.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Inequalities
Graphing
Formulas
Slope-intercept form: y = mx + b
Theorems
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Suitable Grade Level
Grades 7-10