Math Problem Statement
How will I graph ; y>4x-2 on a #line
Solution
To graph the inequality on a coordinate plane, follow these steps:
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Start by graphing the boundary line: The boundary for this inequality is the line . This line is where equals . To graph it:
- Choose two values of , and calculate the corresponding values.
- For , (Point: )
- For , (Point: )
- Plot these points on the coordinate plane and draw the line that passes through them.
- Use a dashed line because the inequality is strict ("greater than" but not "equal to"), so points on the line itself are not included in the solution.
- Choose two values of , and calculate the corresponding values.
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Shade the region above the line: The inequality is , meaning you want the region where is greater than the value of . To do this:
- Pick a test point that is not on the line, such as .
- Substitute and into the inequality: , which is true.
- Since the point satisfies the inequality, shade the region above the dashed line.
This shaded region represents all the points where is greater than .
Would you like a more detailed explanation or help with another graphing concept?
Here are 5 questions that expand on this topic:
- How do you graph inequalities with different slopes?
- How does shading change if the inequality symbol is "less than" instead of "greater than"?
- What does the graph look like if the inequality were instead of ?
- How do you graph inequalities involving vertical or horizontal lines?
- How would the graph change if the slope of the line was negative?
Tip: Always use a dashed line for inequalities that are "strict" (e.g., or ) and a solid line for "inclusive" inequalities (e.g., or ).
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Math Problem Analysis
Mathematical Concepts
Algebra
Graphing Linear Inequalities
Formulas
y = mx + b (Slope-Intercept Form)
Theorems
Graphing Inequalities
Boundary Line and Shading
Suitable Grade Level
Grades 8-10