Math Problem Statement
Solution
I see that you've uploaded an image of a graph of a linear inequality. Let's go step by step to determine the inequality in slope-intercept form.
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Identify the slope and y-intercept:
- The line seems to pass through the y-axis at (0, 3), which means the y-intercept .
- The slope is determined by identifying two points on the line. I see that the line goes through the point (0, 3) and another point like (2, 1). The slope is calculated as: Using the points (0, 3) and (2, 1), the slope calculation is:
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Write the equation: Now, we have the slope and the y-intercept . The equation of the line in slope-intercept form is:
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Determine the inequality: Since the graph shows a dashed line, this indicates that the inequality is strict (i.e., or , not or ). Also, the shading is above the line, which indicates that the solution is for values greater than the line. Hence, the inequality is:
So, the inequality in slope-intercept form is:
Would you like any further clarification on this process? Let me know if you need more details!
Further Questions:
- How do you calculate the slope when the points on the line are not given?
- What does the dashed line indicate in terms of the inequality?
- How can you interpret the shaded region in relation to the inequality?
- How would the inequality change if the line were solid instead of dashed?
- What is the difference between linear equations and linear inequalities?
Tip: To find the slope, always use two points on the line and apply the formula .
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Math Problem Analysis
Mathematical Concepts
Linear Inequalities
Slope-Intercept Form
Graphing Inequalities
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-Intercept form: y = mx + b
Theorems
Linear Inequality Graphing
Suitable Grade Level
Grades 7-9