Math Problem Statement
for 11 12 13 and 14 Next 4 answers should be in the form of y first...then the inequality sign...then the rest of the answer in slope intercept form
Solution
Here are the inequalities for each graph in the form you requested, with first:
11.
The line has a negative slope and the shading is below the line:
12.
The line has a positive slope and the shading is above the line:
13.
The line has a positive slope, and the shading is above the dashed line:
14.
The line has a negative slope and the shading is below the line:
Would you like any further explanations on how these inequalities were derived, or details on the graph interpretations?
Here are 5 related questions that expand on this topic:
- How do you determine the slope of a line from a graph?
- What does a solid line versus a dashed line indicate in an inequality?
- How do you decide which side of the line to shade for an inequality?
- Can you convert these inequalities into standard form?
- How do these inequalities change if the inequality sign is flipped?
Tip: When graphing inequalities, always check if the inequality includes the boundary (solid line for or ) or if it excludes the boundary (dashed line for or ).
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Math Problem Analysis
Mathematical Concepts
Algebra
Graphing Linear Inequalities
Slope-Intercept Form
Formulas
y = mx + b for slope-intercept form
Slope formula: (change in y) / (change in x)
Theorems
Linear Inequality Theorem
Suitable Grade Level
Grades 9-11
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