Math Problem Statement
This is the graph of a linear inequality. Write the inequality in slope-intercept form.
Solution
To find the inequality representing this graph, let's analyze it step-by-step.
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Identify the Line:
- The line appears to pass through points and .
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Calculate the Slope:
- Slope .
- Using points and :
So, the slope of the line is .
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Find the Equation of the Line:
- Using the slope and the y-intercept at , the equation of the line is:
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Determine the Inequality Symbol:
- The shaded region is above the line, which suggests a "greater than" inequality.
- Since the line is solid, it includes points on the line, meaning we use "greater than or equal to."
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Final Inequality:
- The inequality in slope-intercept form is:
Answer
The inequality that represents this graph is:
Would you like more details, or do you have any questions?
Related Questions:
- How would the inequality change if the shaded area were below the line?
- What if the line were dashed instead of solid—how would that affect the inequality?
- How can you verify which side of the line represents the solution to the inequality?
- How does changing the slope affect the position of the shaded region?
- What are the steps to determine the equation of a line in general?
Tip: Always check the shading to determine whether to use or in inequalities.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Inequalities
Graphing
Formulas
Slope formula m = (y2 - y1) / (x2 - x1)
Slope-intercept form y = mx + b
Theorems
Slope-intercept form of a linear equation
Suitable Grade Level
Grades 7-9