Math Problem Statement
Alexander graphed a linear inequality on the coordinate plane.
Which inequality is best represented by the graph? A.y < 32x −3
B.y > 32x −3
C.y > 23x −3
D.y < 23x −3
Solution
To identify which inequality is represented by Alexander's graph, here’s what we should consider:
-
Slope of the Line: In each option, the slope (m) and y-intercept (b) vary. We need to find the correct combination of these values.
-
Inequality Sign: The inequality symbol (
<
or>
) affects whether the shading is above or below the line. Ify >
ory ≥
, the shading will be above the line; ify <
ory ≤
, the shading will be below the line. -
Testing the Options:
- Options A and B have a slope of and a y-intercept of -3.
- Options C and D have a slope of and a y-intercept of -3.
Without the graph, a more specific answer can’t be confirmed, but if you can provide any details on the shading and direction of the line, I can determine the exact inequality.
Would you like further clarification or assistance on how these inequalities would look on a graph?
Further Questions
- What does the graph reveal about the position of the shaded area relative to the line?
- Can you identify the slope and y-intercept on the graph to assist in narrowing down the options?
- Do you observe a dashed or solid line in the graph?
- Is the shaded area above or below the line in the graph?
- How would you graph a similar inequality from scratch?
Tip: Remember that the inequality direction (<
or >
) directly impacts the shading placement on the graph.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Inequalities
Graphing
Formulas
y = mx + b for line equation
Inequality symbols for shading
Theorems
Slope-intercept form
Properties of inequalities in graphing
Suitable Grade Level
Grades 8-10
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