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:

  1. 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.

  2. Inequality Sign: The inequality symbol (< or >) affects whether the shading is above or below the line. If y > or y ≥, the shading will be above the line; if y < or y ≤, the shading will be below the line.

  3. Testing the Options:

    • Options A and B have a slope of 32\frac{3}{2} and a y-intercept of -3.
    • Options C and D have a slope of 23\frac{2}{3} 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

  1. What does the graph reveal about the position of the shaded area relative to the line?
  2. Can you identify the slope and y-intercept on the graph to assist in narrowing down the options?
  3. Do you observe a dashed or solid line in the graph?
  4. Is the shaded area above or below the line in the graph?
  5. 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